Can I put the proofs to my lemmas/theorems/corollaries in my appendix? I have proofs that run on for up to 10 pages. To aid in readability, I would like to discuss my theorem, and the lemmas that support it, without the noise of these lengthy proofs. Can I move the proofs to my lemmas, theorem, etc., into an appendix? Or somewhere else more appropriate?
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.