'X-Men' Director Bryan Singer -- I Wasn't In Hawaii During Alleged Sexual Assault -- and I Have Proof

Bryan Singer believes he has proof that will blow his sexual accuser out of the water ... he was NOT in Hawaii during the period he allegedly committed a sexual assault.

Michael Egan claims in a new lawsuit Singer anally raped him and forced hard drugs on him during 2 separate trips to Hawaii in August and October, 1999.

Sources connected with Singer tell TMZ ... the "X-Men" director has proof he was NOT in Hawaii during that period ... he was in Toronto shooting the first "X-Men" movie.

We're told Singer will file credit card bills and various other documents proving he was in Toronto during the times in question.

We know the movie itself was shot Sept. 22 - March 3 in Toronto, but there was pre-production and we're told Singer was present.