Also, in terms of the broader issue of authority, Schaff writes (and provides documentation):
But the first pope, in the proper sense of the word, is Leo I., who justly bears the title of “the Great” in the history of the Latin hierarchy. In him the idea of the Papacy, as it were, became flesh and blood. He conceived it in great energy and clearness, and carried it out with the Roman spirit of dominion, so far as the circumstances of the time at all allowed. He marks the same relative epoch in the development of the papacy, as Cyprian in the history of the episcopate. He had even a higher idea of the prerogatives of the see of Rome than Gregory the Great, who, though he reigned a hundred and fifty years later, represents rather the patriarchal idea than the papal. Leo was at the same time the first important theologian in the chair of Rome, surpassing in acuteness and depth of thought all his predecessors, and all his successors down to Gregory I. Benedict XIV. placed him (a.d. 1744) in the small class of doctores ecclesiae, or authoritative teachers of the catholic faith. He battled with the Manichaean, the Priscillianist, the Pelagian, and other heresies, and won an immortal name as the finisher of the orthodox doctrine of the person of Christ.
...[Leo] was animated with the unwavering conviction that the Lord himself had committed to him, as the successor of Peter, the care of the whole church. He anticipated all the dogmatical arguments by which the power of the papacy was subsequently established. He refers the petra, on which the church is built, to Peter and his confession. Though Christ himself—to sum up his views on the subject—is in the highest sense the rock and foundation, besides which no other can be laid, yet, by transfer of his authority, the Lord made Peter the rock in virtue of his great confession, and built on him the indestructible temple of his church. [etc., etc.]
...Leo thus made out of a primacy of grace and of personal fitness a primacy of right and of succession. Of his person, indeed, he speaks in his sermons with great humility, but only thereby the more to exalt his official character. He tells the Romans, that the true celebration of the anniversary of his accession is, to recognize, honor, and obey, in his lowly person, Peter himself, who still cares for shepherd and flock, and whose dignity is not lacking even to his unworthy heir. Here, therefore, we already have that characteristic combination of humility and arrogance, which has stereotyped itself in the expressions: “Servant of the servants of God,” “vicar of Christ,” and even “God upon earth.” In this double consciousness of his personal unworthiness and his official exaltation, Leo annually celebrated the day of his elevation to the chair of Peter.
