Peter doesn't just present abstract facts. He makes it personal, appealing directly to the listeners' own experience. Why is this direct appeal so powerful?
The verse ends with a powerful, direct appeal: 'as you yourselves also know.' Peter isn't asking them to believe something based on hearsay. He's telling them that the very things they witnessed firsthand serve as undeniable proof.
This is key to Peter's argument. The miracles, wonders, and signs weren't performed in secret; they happened 'in your midst.' Many of those listening would have seen Jesus heal people, cast out demons, or perform other astounding acts. Even if they didn't believe he was the Messiah then, they couldn't deny that Jesus possessed extraordinary power, and that this power came from God.
Peter is essentially saying: 'You saw it with your own eyes. You know these things happened. Don't ignore the evidence you already possess. Let that knowledge lead you to the truth about Jesus.'