There's no evidence for that from the Bible, either, is there. :-0
However, not only do we not wish to provide any evidence that Peter was not the Bishop of Antioch, we'll positively insist that he was the Bishop of Antioch ... before he turned over that See to another man, and went to Rome.
So then you disagree with that great Catholic scholar F.A. Sullivan who insists that Apostles were never Bishops and vice versa?