Saint Irenaeus of Lyons wrote in AD 190:
"Since, however, it would be very tedious, in such a volume as this, to reckon up the successions of all the Churches, we do put to confusion all those who, in whatever manner, whether by an evil self-pleasing, by vainglory, or by blindness and perverse opinion, assemble in unauthorized meetings; by indicating that tradition derived from the apostles, of the very great, the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul; as also the faith preached to men, which comes down to our time by means of the successions of the bishops. For it is a matter of necessity that every Church should agree with this Church, on account of its preeminent authority, that is, the faithful everywhere, inasmuch as the tradition has been preserved continuously by those who exist everywhere."
200 years later, the Roman Emperors ordered the entire Empire to submit to the Church of Rome, which alone had remained pure and undefiled against the Arian heretics, declaring in the Edict of Thessalonica:
It is our desire that all the various nations which are subject to our Clemency and Moderation, should continue to profess that religion which was delivered to the Romans by the divine Apostle Peter, as it has been preserved by faithful tradition, and which is now professed by the Pontiff Damasus and by Peter, Bishop of Alexandria, a man of apostolic holiness.
That Rome's authority comes not from man, nor any council, but from the Lord Jesus Christ himself, was acknowledged before all at the Council of Ephesus in AD 431:
There is no doubt, and in fact it has been known in all ages, that the holy and most blessed Peter, prince and head of the Apostles, pillar of the faith, and foundation of the Catholic Church, received the keys of the kingdom from our Lord Jesus Christ, the Saviour and Redeemer of the human race, and that to him was given the power of loosing and binding sins: who down even to today and forever both lives and judges in his successors. The holy and most blessed pope Cœlestine, according to due order, is his successor and holds his place.
At the Council of Chalcedon in AD 451, the Pope was called "the ruler of the whole Church", and the text of the First Council of Nicea (AD 325) was read, which stated "The Roman Church has always had the primacy." In response, the council declared:
From what has been done and brought forward on each side, we perceive that the primacy of all and the chief honour according to the canons, is to be kept for the most God-beloved archbishop of Old Rome.
Now the council of Chalcedon attempted to elevate the see of Constantinople, capital of the Byzantine Empire, to a place of honor equal to Rome. But they had to seek permission from the Bishop of Rome, writing:
And this golden chain leading down from the Author of the command to us, you yourself have steadfastly preserved, being set as the mouthpiece unto all of the blessed Peter, and imparting the blessedness of his Faith unto all... Of whom you were chief, as the head to the members, showing your goodwill in the person of those who represented you... Accordingly, we entreat you, honour our decision by your assent, and as we have yielded to the head our agreement on things honourable, so may the head also fulfil for the children what is fitting.
Pope Leo I sternly rebuked the council for attempting to elevate Constantinople above the churches of Alexandria, Antioch and Jerusalem, whose sees were given a place of honor after Rome at the First Council of Nicea. Eventually all out schism broke out between Rome and Constantinople - the Acacian Schism - but in the end Constantinople and the other eastern churches submitted to Rome (the "Apostolic See") in the Formula of Hormisdas, which declared:
For it is impossible that the words of our Lord Jesus Christ, who said, "Thou art Peter, and upon this rock I will build my Church," , should not be verified. And their truth has been proved by the course of history, for in the Apostolic See the Catholic religion has always been kept unsullied.
Following, as we have said before, the Apostolic See in all things and proclaiming all its decisions, we endorse and approve all the letters which Pope St Leo wrote concerning the Christian religion. And so I hope I may deserve to be associated with you in **the one communion which the Apostolic See proclaims, in which the whole, true, and perfect security of the Christian religion resides**. I promise that from now on **those who are separated from the communion of the Catholic Church, that is, who are not in agreement with the Apostolic See,** will not have their names read during the sacred mysteries.