The boldness of Peter encouraged John to enter the tomb and very probably the fast running of John had spurred Peter to even greater speed than he thought himself capable of. Again, it is the same with us in our Christian walk (Heb 10:24-25).

Hebrews 10:24-25  And let us consider how we may spur one another on towards love and good deeds.  Let us not give up meeting together, as some are in the habit of doing, but let us encourage one another—and all the more as you see the Day approaching.

Peter saw more after he entered than John did in his stooping glance from outside the tomb, but John saw the meaning and implications of it better than Peter. John saw and “believed” but Peter saw and went away “marveling” or “wondering” (Luke 24:12). Robertson wryly observes that “Peter had more sight, John more insight.” Henry wonders if “A mind disposed to contemplation may perhaps sooner receive the evidence of divine truth than a mind disposed to action.” True or not, John was the first one to believe that Jesus had risen from the dead even before he saw Him.

Luke 24:12  Peter, however, got up and ran to the tomb. Bending over, he saw the strips of linen lying by themselves, and he went away, wondering to himself what had happened.

Some have felt that the recording of this fact shows a certain amount of pride, but in view of what Jesus says in verse 20:29 it is more likely humility. Why?

John 20:29  Then Jesus told him, “Because you have seen me, you have believed; blessed are those who have not seen and yet have believed.”

Note that Peter and John did not see the angels but the women did. We would have thought that God would make a greater display to those in positions of authority than those who were not, but God doesn’t usually work that way.