He doesn't have to "prove" them to investigate them. He is simply highlighting he would have the right to do that...You realize this is likely a redux of "lock her up," right? The minions get entertained, Trump gets to make unproven allegations, and at the end of the day he does nothing. Why? Because he knows if he tries to prosecute it will blow up in his face.
It's much more effective to keep the lie alive so the rubes go to bed dreaming of the day Hillary goes to jail.