Origen — as excerpted in the Catena Aurea on John 13:12-20

“(t. xxxii. 9.) That ye may believe, is not said, as if the Apostles did not believe already, but is equivalent to saying, Do as ye believe, and persevere in your belief, seeking for no occasion of falling away. For besides the evidences the disciples had already seen, they had now that of the fulfilment of prophecy.”