A B737 FLT CREW THOUGHT THEY WERE CLRED TO CROSS RWY 24L AT LAX ONLY TO FIND OUT BY TWR THAT THEY WERE NOT.

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WE LANDED NORMALLY ON RWY 22R AT LAX. ON LNDG ROLL; WE WERE TOLD TO EXIT RWY 24R AND HOLD SHORT OF RWY 24L. WE ACKNOWLEDGED THE HOLD SHORT INSTRUCTIONS. A FEW MINS LATER ON TXWY AA; THE CAPT ASKED ME IF WE WERE CLRED TO CROSS RWY 24L. I RESPONDED WITH 'YES.' ONCE CLR OF RWY 24L; GND CTL ASKED US TO CALL THEM AT THE GATE. ONCE AT THE GATE WE FOUND OUT WE HAD CROSSED WITHOUT CLRNC. WHEN THE CAPT ASKED ME IF WE WERE CLRED TO CROSS RWY 24L (AT THE TIME I WAS POSITIVE WE WERE); HE CAUSED ME TO BEGIN TO DOUBT MYSELF. THE JET WAS STILL ROLLING (ON TXWY AA) AND WHILE I REPLAYED THE RADIO CALLS IN MY HEAD; WE VISUALLY CLRED RWY 24L FROM TXWY AA. WE SAW NOTHING ON THE RWY; SO WE CROSSED. THE CAPT CONTINUING ACROSS PUT MY MIND AT EASE. AS I RETHINK THROUGH THE SCENARIO; A FEW THINGS COME TO MIND. FIRST; THERE WAS A LOT OF CHATTER ON THE RADIOS; AND SECONDLY IT WAS A GOOD BIT OF TIME FROM THE INITIAL HOLD SHORT INSTRUCTIONS; UNTIL WE WERE ACTUALLY ON TXWY AA. I DO NOT KNOW WHY WE FELT WE WERE CLRED TO CROSS -- POSSIBLY ALL THE RADIO CHATTER. WHAT REALLY MAKES ME MAD IS WHEN THE CAPT ASKED THE QUESTION AND RAISED A SMALL PERCENTAGE OF DOUBT; I LET OUR VISUAL CHK OF THE RWY CLR UP THE DOUBT. I SHOULD HAVE DONE WHAT I NORMALLY DO; WHICH IS TO VERIFY VERBALLY. I AM MAD AT MYSELF FOR LETTING THE FACT THAT THE RWY WAS CLR; CONVINCE ME THAT I WAS RIGHT -- WHEN IN REALITY I WAS WRONG. WHEN IN DOUBT; VERIFY!