No Bishop Of Bishops

"For neither does any of us set himself up as a bishop of bishops, nor by tyrannical terror does any compel his colleague to the necessity of obedience; since every bishop, according to the allowance of his liberty and power, has his own proper right of judgment, and can no more be judged by another than he himself can judge another. But let us all wait for the judgment of our Lord Jesus Christ, who is the only one that has the power both of preferring us in the government of His Church, and of judging us in our conduct there." (Cyprian)

As you can see on the page linked above, dozens of other bishops at the council spoke after Cyprian made his comments. Nobody voiced any disagreement with what he said. They often appeal to scripture and reason to justify their position on the matter before them, but nobody appeals to papal authority. And nobody gives any indication of thinking that such an office existed or that departing from it or operating independently of it needed to be justified.