MLG FLC TAXIES ACROSS RWY FOR WHICH CLRED TO HOLD SHORT.

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WE WERE ISSUED TAXI INSTRUCTIONS TO THE ACTIVE RWY WHICH WAS 27L. THE TAXI CLRNC WAS TO UTILIZE TAXIWAY XRAY HOLD SHORT OF 27R FOR TKOF ON 27L. THE PRECEDING CLRNC WAS ONLY PARTIALLY HEARD BY ME (THE CAPT). AS WE WERE TAXIING ALONG XRAY AND APCHING 27R; I ASKED MY FO IF WE WERE CLRED 'ALL THE WAY OUT.' HE RESPONDED 'YES.' I LOOKED BOTH DIRECTIONS BEFORE XING 27R. THERE WAS 1 ACFT ON AN EXTENDED R BASE FOR 27R WHICH I CONSIDERED NO FACTOR SO WE PROCEEDED TO CROSS 27R ENRTE TO 27L. AFTER WE CROSSED 27R; GND CTL SAID WE WERE NOT CLRED TO CROSS 27R. I LOOKED AT MY FO IN DISBELIEF. HOW COULD HE LET ME CROSS WITHOUT BEING CERTAIN? AT THIS POINT I REALIZED WE BOTH MADE CRUCIAL MISTAKES AND WE'RE VERY FORTUNATE DANGER WAS NOT A FACTOR. MY FO MADE 2 CRITICAL ERRORS. FIRST HE DID NOT REMEMBER THE ISSUED CLRNC AND READBACK AND SECOND; HE GAVE AN AFFIRMATIVE ANSWER TO A DIRECT QUESTION 'ARE WE CLRED ALL THE WAY OUT?' AS CAPT; MY MISTAKES WERE NOT HEARING THE TAXI INSTRUCTION AND READBACK; AND SECONDLY; WHEN I HAD DOUBT ON XRAY I SHOULD HAVE KEYED THE MIKE AND QUERIED GND CTL MYSELF ELIMINATING POSSIBILITY FOR HUMAN ERROR.