Referee says the proof is wrong, but it is not, what to do?
While you might be able to appeal to the editor, once you've been rejected, you're probably not going to get a change in decision.  I would instead recommend focusing on a new submission to another journal.

Before you do so, however, I would strongly advise performing a major revision on your presentation of the proofs.  Assuming that your proofs are in fact correct, you clearly did not convey them in such a way that their correctness and significance were obvious to the reviewer.  The reviewer may have been a sloppy or shallow reader, but so in fact will be many of your other readers after publication.  

In short, take the feedback as an indicator of how your paper needs to be improved before you submit it to another journal.