John 20:6

Then cometh Simon Peter following him, and went into the sepulchre. Peter (says S. Chrysostom) entered with ardour, and carefully inspected everything. For the soldiers who guarded the tomb, when they saw the angel and the earthquake, ran away through fear. See also S. Jerome, Quæst. vi . ad Hedib. And seeth the linen clothes lie, and the napkin which was about His head (covering His face, as is generally done to the dead, for the sake of seemliness), not lying with the linen clothes, but wrapped together in a place by itself. "This," says S. Chrysostom, "was a sign of His Resurrection, for if they had removed the body they would not have stripped it, and if they had stolen it, they would not have been so careful to fold up the napkin, and put it aside by itself; for John had said before that He was buried with myrrh, which makes linen clothes cling close to the body, so that no one would be deceived by those who said that It was stolen away; for what thief would trouble himself so much about an unnecessary matter?" Ver. 8. Then went in also that other disciple, which came first to the sepulchre.

Tropologically, Toletus says that by John are signified all Christians, but by Peter the Pontiffs, Vicars of Christ. Peter then entered the tomb first as the highest in dignity, as the Vicar of Christ; but John came last, because it is possible that he who is first in rank, is behind others in desert and holiness.

And he saw and believed. Both of them, that is, believed that what Mary Magdalene said was true, namely, that the Body of Christ had been taken away. So says S. Augustine, Theophylact, and Jansen. S. Cyril, Chrysostom, Euthymius, and Nyssen add that both believed that Christ had risen. But this word "believed" more clearly and correctly applies only to S. John, who remembered the words of Christ, that He would rise on the third day. But Peter, on account of the strangeness of a Resurrection, and from His earnest desire to see Him alive again, was more slow to believe that Christ had risen. Whence the Angel significantly said to the women, "Go, tell His disciples and Peter." (Mark 16:7.) Ver. 9. For as yet they knew not the scriptures, that He must rise again from the dead. For although He had solemnly assured them that He would rise, yet on account of its strange and wonderful nature they believed it not, but thought that He spoke in a figure and parable, as He was wont to do. Ver. 10. Then the disciples went away again unto their own home. Peter wondering, John believing He had risen, the Magdalene alone remaining at the sepulchre, to learn something more certain about the Body of her beloved Christ. See S. Augustine (in loc.) "And hence it came to pass that she alone saw Him, she who remained to seek for Him, for perseverance in a good work is a virtue," says S. Gregory, Hom. xxv.