Can I put the proofs to my lemmas/theorems/corollaries in my appendix?
Can I move the proofs to my lemmas, theorem, etc., into an appendix? 


Yes - this is often done in journal articles. You might want to put a sketch of why your claims should be believed in the main text, with a pointer to the full proofs in the appendix.

But, you have tagged this thesis, so it would be worth discussing this with your thesis advisor, as they may have a different opinion for your particular field or their particular preferences/style.