A WDB ACR CREW FAILED TO CHK THEIR MEL PRIOR TO TKOF AND FLEW IN AN ILLEGAL CONDITION.

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WE WERE UNABLE TO MAKE CONTACT WITH GND CTL USING THE #1 VHF RADIO. BOTH #2 AND #3 VHF WERE WORKING JUST FINE. AFTER PUSHBACK WAS COMPLETE; WE DETERMINED THE #1 VHF RECEIVER WAS OK. I REASONED WITH WHAT SEEMED LIKE SOUND LOGIC AT THE TIME; THAT WITH #3 VHF RADIOS; 1 OF THEM COULD BE INOP FOR A LEGAL DISPATCH WITHOUT A SPECIAL RELEASE. I ORDINARILY WOULD HAVE; AND SHOULD HAVE; CHKED THE MEL BEFORE CONTINUING. HOWEVER; I WAS TOO CONCERNED ABOUT THE POTENTIAL DELAY AND POSSIBLY LOSING THE 'PREFERRED' ALT WE HAD RECEIVED WITH OUR ATC CLRNC. CHKING THE MEL AFTER LEVEL OFF AT CRUISE; I DISCOVERED MUCH TO MY CHAGRIN THAT VHF #1 WAS REQUIRED UNLESS DISPATCHED IN VMC. ONLY #2 OR #3 VHF COULD BE INOP. OUR FLT CONTINUED ON TO DEST WITHOUT INCIDENT. ON ARR; MAINT REPLACED THE #1 VHF RADIO. I REVIEWED THE ACFT ELECTRICAL SYS AS IT PERTAINS TO THE #1 VHF RADIO AND DISCOVERED THE OBVIOUS LOGIC FOR THE MEL RESTRICTION. I REALLY FEEL STUPID AND I HAVE PLEDGED TO MYSELF TO NEVER RELY ONLY ON MY LOGIC! I WILL TAKE THE TIME TO CAREFULLY CHK THE MEL. P.S. THE #1 VHF RADIO PROB WAS AN INTERMITTENT XMITTER. AS YOU MIGHT GUESS; IT WORKED PERFECTLY FOR MAINT ON ARR BUT NEVERTHELESS THEY REPLACED THE ENTIRE RADIO.