But something did change:
So the fathers of the fourth council of Constantinople, following the footsteps of their predecessors, published this solemn profession of faith:
The first condition of salvation is to maintain the rule of the true faith. And since that saying of our lord Jesus Christ, You are Peter, and upon this rock I will build my church [55] , cannot fail of its effect, the words spoken are confirmed by their consequences. For in the apostolic see the catholic religion has always been preserved unblemished, and sacred doctrine been held in honour. Since it is our earnest desire to be in no way separated from this faith and doctrine, we hope that we may deserve to remain in that one communion which the apostolic see preaches, for in it is the whole and true strength of the christian religion [56] .
What is more, with the approval of the second council of Lyons, the Greeks made the following profession:
“The holy Roman church possesses the supreme and full primacy and principality over the whole catholic church. She truly and humbly acknowledges that she received this from the Lord himself in blessed Peter, the prince and chief of the apostles, whose successor the Roman pontiff is, together with the fullness of power. And since before all others she has the duty of defending the truth of the faith, so if any questions arise concerning the faith, it is by her judgment that they must be settled.” [57]
Also,
It was for this reason that the bishops of the whole world, sometimes individually, sometimes gathered in synods, according to the long established custom of the churches and the pattern of ancient usage referred to this apostolic see those dangers especially which arose in matters concerning the faith. This was to ensure that any damage suffered by the faith should be repaired in that place above all where the faith can know no failing [59] .