Augustine of Hippo — as excerpted in the Catena Aurea on John 13:6-11

“(Ad. Seleuc. Ep. c. viii.) From what is here said, we understand that Peter was already baptized. Indeed that He baptized by His disciples, shews that His disciples must have been baptized, either with John’s baptism, or, which is more probable, Christ’s. He baptized by means of baptized servants; for He did not refuse the ministry of baptizing, Who had the humility to wash feet.”