“Furthermore, we declare, we proclaim, we define that it is absolutely necessary for salvation that every human creature be subject to the Roman Pontiff.”

— Pope Boniface VIII, Unam Sanctam

“Furthermore, in this one Church of Christ no man can be or remain who does not accept, recognize and obey the authority and supremacy of Peter and his legitimate successors. Did not the ancestors of those who are now entangled in the errors of Photius and the reformers, obey the Bishop of Rome, the chief shepherd of souls? Alas their children left the home of their fathers, but it did not fall to the ground and perish for ever, for it was supported by God. Let them therefore return to their common Father, who, forgetting the insults previously heaped on the Apostolic See, will receive them in the most loving fashion. For if, as they continually state, they long to be united with Us and ours, why do they not hasten to enter the Church, “the Mother and mistress of all Christ’s faithful”?[25] Let them hear Lactantius crying out: “The Catholic Church is alone in keeping the true worship. This is the fount of truth, this the house of Faith, this the temple of God: if any man enter not here, or if any man go forth from it, he is a stranger to the hope of life and salvation. Let none delude himself with obstinate wrangling. For life and salvation are here concerned, which will be lost and entirely destroyed, unless their interests are carefully and assiduously kept in mind.”

— Pope Pius XI, Mortalium Animos

“The Church’s constant missionary proclamation is endangered today by relativistic theories which seek to justify religious pluralism, not only de facto but also de iure (or in principle). As a consequence, it is held that certain truths have been superseded; for example, the definitive and complete character of the revelation of Jesus Christ, the nature of Christian faith as compared with that of belief in other religions, the inspired nature of the books of Sacred Scripture, the personal unity between the Eternal Word and Jesus of Nazareth, the unity of the economy of the Incarnate Word and the Holy Spirit, the unicity and salvific universality of the mystery of Jesus Christ, the universal salvific mediation of the Church, the inseparability — while recognizing the distinction — of the kingdom of God, the kingdom of Christ, and the Church, and the subsistence of the one Church of Christ in the Catholic Church.

[…]

Therefore, in connection with the unicity and universality of the salvific mediation of Jesus Christ, the unicity of the Church founded by him must be firmly believed as a truth of Catholic faith. Just as there is one Christ, so there exists a single body of Christ, a single Bride of Christ: “a single Catholic and apostolic Church”. Furthermore, the promises of the Lord that he would not abandon his Church (cf. Mt 16:18; 28:20) and that he would guide her by his Spirit (cf. Jn 16:13) mean, according to Catholic faith, that the unicity and the unity of the Church — like everything that belongs to the Church’s integrity — will never be lacking.
The Catholic faithful are required to profess that there is an historical continuity — rooted in the apostolic succession — between the Church founded by Christ and the Catholic Church: “This is the single Church of Christ… which our Saviour, after his resurrection, entrusted to Peter’s pastoral care (cf. Jn 21:17), commissioning him and the other Apostles to extend and rule her (cf. Mt 28:18ff.), erected for all ages as ‘the pillar and mainstay of the truth’ (1 Tim 3:15). This Church, constituted and organized as a society in the present world, subsists in [subsistit in] the Catholic Church, governed by the Successor of Peter and by the Bishops in communion with him”.

–Congregation for the Doctrine of the Faith, Dominus Iesus