That which the Prince of Shepherds and great Shepherd of the sheep, Jesus Christ our Lord, established in the person of the Blessed Apostle Peter to secure the perpetual welfare and lasting good of the Church, must, by the same institution, necessarily remain unceasingly in the Church; which, being founded upon the Rock, will stand firm to the end of the world. For none can doubt, and it is known to all ages, that the holy and Blessed Peter, the Prince and Chief of the Apostles, the pillar of the faith and foundation of the Catholic Church, received the keys of the kingdom from Our Lord Jesus Christ, the Savior and Redeemer of mankind, and lives, presides, and judges, to this day and always, in his successors the Bishops of the Holy See of Rome, which was founded by him, and consecrated by his blood.
Thus, whosoever succeeds Peter in this Chair, obtains, by the institution of Christ Himself, the Primacy of Peter over the whole Church. Therefore, the disposition of truth remains, and Blessed Peter, persevering in the fortitude of the Rock that he accepted, has not relinquished the governance of the Church that he received.
Therefore, it has always been necessary that each Church — that is, those who are the faithful everywhere — should agree with the Roman Church, because of the greater power of the principality that She has received, in order that, all being joined together in the unity of that Seat, from the veneration of which the rights of communion flows to all, might associate closely as members of one Head, in the compact unity of the body.
‘If then, any should deny that it is by the institution of Christ the Lord and by Divine right, that Blessed Peter should have a perpetual line of successors in the Primacy over the Universal Church, or that the Roman Pontiff’ is the successor of Blessed Peter in this primacy; let him be anathema. — Vatican Council, Pastor Aeternus