For although it is evident from the word of the Lord Himself in the Sacred Gospel [cf. Mt 16:18] where the Church is established, let us hear nevertheless what the Blessed Augustine, mindful of the opinion of the same Lord, has explained. For he says that the Church of God is established among those who are known to preside over the apostolic sees through the succession of those in charge, and whoever separates himself from the communion or authority of these sees, is shown to be in schism. And following additional remarks (he says): "If you are put outside, for the Name of Christ you will also die. Suffer for Christ among the members of Christ; clinging to the body, fight for the Head." But the Blessed Cyprian ... among other things, says the following: "The beginning starts from unity, and the primacy is given to PETER, so that the Church and the chair of Christ may be shown (to be) one: and they are all shepherds, but the flock, which is fed by the Apostles in unanimous agreement, is shown to be one." And after a few (remarks he adds): "Does he who does not hold this unity of the Church believe that he has the faith? Does he who deserts and resists the chair of PETER, on which the Church was founded, have confidence that he is in the Church?" Likewise after other remarks (he asserts): "They cannot arrive at the reward of peace, because they disrupt the peace of the Lord by the fury of discord. ... Those who were not willing to be at agreement in the Church of God, cannot remain with God; although given over to flames and fires, they burn, or thrown to wild beasts, they lay down their lives, there will not be [for them] that crown of faith, but the punishment of faithlessness, not a glorious result (of religious virtue), but the ruin of despair. Such a one can be slain, he cannot be crowned. ... For the crime of schism is worse than that which they [commit] who have offered sacrifice, who, nevertheless, having been disposed to penance for their sins prayed to God with the fullest satisfaction. In this case the Church is sought and solicited; in the other the Church is opposed. So in this case he who has fallen, has injured only himself; in the other, who attempts to cause a schism deceives many by dragging (them) with himself. In this case there is the loss of one soul; in the other there is danger to many. Certainly the one knows that he has sinned and laments and bewails (it); the other puffed up with pride in his sin and pluming himself on the sins themselves, separates sons from their mother, seduces the sheep from the shepherds, disturbs the Sacraments of God, and, whereas the former having stumbled sinned once, the latter sins daily. Lastly although the lapsed, if afterwards he acquired martyrdom, is able to secure the promises of the Kingdom; if the other is slain outside of the Church, he cannot attain to the rewards of the Church."
Denzinger 423: Pope Innocent III of Rome (1198-1216) on 12/18/1208, Profession of Faith Prescribed for Durand of Osca and his Waldensian Companions, from the letter "Fitts exemplo" to the Archbishop of Terraco: "By the heart we believe and by the mouth we confess the one Church, not of heretics but the Holy Roman, Catholic, and Apostolic (Church) outside which we believe that no one is saved."
Denzinger 430: Twelfth Ecumenical Council (Lateran IV in 1215 under Pope Innocent III), Definition directed against the Albigensians and other heretics: One indeed is the universal Church of the faithful, outside which no one at all is saved, in which the priest himself is the sacrifice, Jesus Christ, Whose Body and Blood are truly contained in the sacrament of the altar under the species of bread and wine; the bread (changed) into His Body by the divine power of transubstantiation, and the wine into the Blood, so that to accomplish the mystery of unity we ourselves receive from His (nature) what He Himself received from ours. And surely no one can accomplish this sacrament except a priest who has been rightly ordained according to the keys of the Church which Jesus Christ Himself conceded to the Apostles and to their successors. But the sacrament of Baptism (which at the invocation of God and the indivisible Trinity, namely, of the Father and of the Son and of the Holy Spirit, is solemnized in water) rightly conferred by anyone in the form of the Church is useful unto salvation for little ones and for adults. And if, after the reception of Baptism, anyone shall have lapsed into sin, through true penance he can always be restored. Moreover, not only virgins and the continent but also married persons pleasing to God through right faith and good work merit to arrive at a blessed eternity.
Denzinger 468-469: Pope Boniface VIII of Rome (1294-1303) on 11/18/1302, Bull "Unam Sanctam":
Urged by faith, we are obliged to believe and to maintain that the Church is one, holy, catholic, and also apostolic. We believe in her firmly and we confess with simplicity that outside of her there is neither salvation nor the remission of sins, as the Spouse in the Canticles [Sgs 6:8] proclaims: "One is my dove, my perfect one. She is the only one, the chosen of her who bore her," and she represents one sole mystical body whose Head is Christ and the head of Christ is God [1 Cor 11:3]. In her then is "one Lord, one faith, one baptism" [Eph 4:5]. There had been at the time of the deluge only one ark of Noah, prefiguring the one Church, which ark, having been finished to a single cubit, had only one pilot and guide, i.e., Noah, and we read that, outside of this ark, all that subsisted on the earth was destroyed. We venerate this Church as one, the Lord having said by the mouth of the prophet: "Deliver, O God, my soul from the sword and my only one from the hand of the dog" [Ps 21:20]. He has prayed for His Soul, that is for Himself, Heart and Body; and this Body, that is to say, the Church, He has called one because of the unity of the Spouse, of the faith, of the Sacraments, and of the charity of the Church. This is the tunic of the Lord, the seamless tunic, which was not rent but which was cast by lot [Jn 19:23-24]. Therefore, of the one and only Church there is one Body and one Head, not two heads like a monster; that is, Christ and the Vicar of Christ, Peter and the successor of Peter, since the Lord speaking to Peter Himself said: "Feed My sheep" [Jn 21:17], meaning, My sheep in general, not these, nor those in particular, whence we understand that He entrusted all to him [Peter]. Therefore, if the Greeks or others should say that they are not confided to Peter and to his successors, they must confess not being the sheep of Christ, since Our Lord says in John "there is one sheepfold and one shepherd." ... Furthermore, we declare, we proclaim, we define that it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff.Denzinger 570B: Pope Clement VI of Rome (1342-1352) on 9/20/1351, Letter "Super quibusdam" to the Consolator, the Armenian Catholicos Mekhitar I of Cilicia (1341-1355): "In the second place, we ask whether you and the Armenians obedient to you believe that no man of the wayfarers outside the faith of this Church, and outside the obedience of the Pope of Rome, can finally be saved."
Denzinger 714: Pope Eugene IV of Rome (1431-1447) on 2/4/1440, Bull "Cantate Domino" at 17th Ecumenical Council (Florence): The most Holy Roman Church firmly believes, professes, and preaches that none of those existing outside the Catholic Church, not only pagans, but also Jews and heretics and schismatics, can have a share in life eternal; but that they will go into the "eternal fire which was prepared for the devil and his angels" (Matthew 25:41), unless before death they are joined with Her; and that so important is the unity of this ecclesiastical body that only those remaining within this unity can profit by the sacraments of the Church unto salvation, and they alone can receive an eternal recompense for their fasts, their almsgivings, their other works of Christian piety and the duties of a Christian soldier. No one, let his almsgiving be as great as it may, no one, even if he pour out his blood for the Name of Christ, can be saved, unless he remain within the bosom and the unity of the Catholic Church.
Denzinger 1473: Pope Benedict XIV of Rome (1740-1758) on 3/16/1743, Profession of Faith prescribed for the Maronites: Likewise, all other things I accept and profess, which the Holy Roman Church accepts and professes, and I likewise condemn, reject, and anathematize, at the same time all contrary things, both schisms and heresies, which have been condemned, rejected, and anathematized by the same Church. In addition, I promise and swear true obedience to the Roman Pontiff, the successor of Blessed Peter, the prince of the Apostles and the vicar of Jesus Christ. And that this faith of the Catholic Church, without which no one can be saved, etc...
Denzinger 1647-1648: Bl. Pope Pius IX of Rome (1846-1878) on 12/9/1854, Allocution "Singulari Quadem": For, it must be held by faith that outside the Apostolic Roman Church, no one can be saved; that this is the only ark of salvation; that he who shall not have entered therein will perish in the flood; but, on the other hand, it is necessary to hold for certain that they who labor in ignorance of the true religion, if this ignorance is invincible, are not stained by any guilt in this matter in the eyes of God. Now, in truth, who would arrogate so much to himself as to mark the limits of such an ignorance, because of the nature and variety of peoples, regions, innate dispositions, and of so many other things? For, in truth, when released from these corporeal chains "we shall see God as He is" [1 Jn 3:2], we shall understand perfectly by how close and beautiful a bond divine mercy and justice are united; but, as long as we are on earth, weighed down by this mortal mass which blunts the soul, let us hold most firmly that, in accordance with Catholic teaching, there is "one God, one faith, one Baptism" [Eph 4:5]; it is unlawful to proceed further in inquiry. ... But, just as the way of charity demands, let us pour forth continual prayers that all nations everywhere may be converted to Christ; and let us be devoted to the common salvation of men in proportion to our strength, "for the hand of the Lord is not shortened" [Is 9:1] and the gifts of Heavenly grace will not be wanting those who sincerely wish and ask to be refreshed by this light. Truths of this sort should be deeply fixed in the minds of the faithful, lest they be corrupted by false doctrines, whose object is to foster an indifference toward religion, which we see spreading widely and growing strong for the destruction of souls.
Denzinger 1677-1678: Bl. Pope Pius IX of Rome (1846-1878) on 8/10/1863, Encyclical Letter "Quanto conficiamur moerore" to the bishops of Italy:
Denzinger 1955: Pope Leo XIII of Rome (1878-1903) on 6/29/1896, Encyclical letter "Satis cognitum" 4-5: Now, if we look at what was done, Jesus Christ did not arrange and organize such a Church as would embrace several communities similar in kind, but distinct, and not bound together by those bonds that make the Church indivisible and unique after that manner clearly in which we profess in the Symbol of Faith, "I believe in one Church." ... Now, Jesus Christ when He was speaking of such a mystical edifice, spoke only of one Church which He called His own: "I will build My Church" [Mt 16:18]. Whatever other church is under consideration than this one, since it was not founded by Jesus Christ, cannot be the true Church of Christ. ... And so the Church is bound to spread among all men the salvation accomplished by Jesus Christ, and all the blessings that proceed therefrom, and to propagate them through the ages. Therefore, according to the will of its Author the Church must be alone in all lands in the perpetuity of time. ... The Church of Christ, therefore, is one and the same for ever; those who leave it depart from the will and command of Christ, the Lord - leaving the path of salvation they enter on that of perdition.
Denzinger 2286: Ven. Pope Pius XII of Rome (1939-1958) on 6/29/1943, Encyclical letter "Mystici Corporis Christi" 22: Actually only those are to be numbered among the members of the Church who have received the laver of regeneration and profess the true faith, and have not, to their misfortune, separated themselves from the structure of the Body, or for very serious sins have not been excluded by lawful authority. "For in one Spirit," says the Apostle, "were we all baptized into one Body, whether Jews or Gentiles, whether bond or free" [1 Cor 12:13]. So, just as in the true community of the faithful of Christ there is only one Body, one Spirit, one Lord, and one Baptism, so there can be only one faith [cf. Eph 4:5]; and so he who refuses to hear the Church, as the Lord bids "let him be as the heathen and publican" [cf. Mt 18:17]. Therefore, those who are divided from one another in faith or in government cannot live in the unity of such a body, and in its one Divine Spirit.
Denzinger 2288: Ibid. 56-57: If we closely examine this divine principle of life and virtue given by Christ, insofar as He established it as the source of every gift and created grace, we easily understand that this is nothing else than the Paraclete, the Spirit, Who proceeds from the Father and the Son, and Who in a special manner is called "the Spirit of Christ," or "the Spirit of the Son" [Rom 8:9; 2 Cor 3:17; Gal 4:6]. For by this Breath of grace and truth did the Son of God anoint His soul in the uncontaminated womb of the Virgin; this Spirit holds it a delight to dwell in the beloved soul of the Redeemer as in His most beloved temple; this Spirit, Christ by shedding His own Blood merited for us on the Cross; this Spirit, finally, when He breathed upon the Apostles, He bestowed on the Church for the remission of sins [cf. Jn 20:22]; and, while Christ alone received this Spirit according to no measure [cf. Jn 3:34], yet to the members of the mystical body He is imparted only according to the measure of the giving of Christ, out of Christ's own fullness [cf. Eph 1:8; 4:7]. And after Christ was glorified on the Cross, His Spirit is communicated to the Church in the richest effusion, that she and her individual members may more and more daily become like our Savior. It is the Spirit of Christ that has made us God's adopted sons [cf. Rom 8:14-17; Gal 4:6-7], that someday "we all beholding the glory of God with open face may be transformed into the the same image from glory to glory" [2 Cor 3:18].
Moreover, to this Spirit of Christ as to no visible principle is this also to be attributed, that all parts of the Body are joined to one another as they are with their exalted Head; for He is entire in the Head, entire in the Body, entire in the individual members, and with these He is present, and these He assists in various ways, according to their various duties and offices, according to the greater or less degree of spiritual health which they enjoy. He is the one Who by His Heavenly grace is to be held as the principle of every vital and in fact every salutary act in all the parts of any body. He is the one Who, although He Himself is present of Himself in all members, and is divinely active in the same, yet in the inferior members also operates through the ministry of the higher members; finally, He is the one Who, while He always day by day produces the growth of the Church by imparting grace, yet refuses to dwell through sanctifying grace in members wholly cut off from the Body. Indeed, the presence and activity of the Spirit of Jesus Christ are succinctly and vigorously expressed by Our most wise predecessor, Leo XIII, of immortal memory in the Encyclical, "Divinum illud," in these words: "Let it suffice to state this, that, as Christ is the Head of the Church, the Holy Spirit is her Soul."