A B737-700 FLT CREW FLEW INTO ICING CONDITIONS WITH AN MEL RESTRICTING SUCH OPS.

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I PICKED UP FLT. ACFT HAD 3 MEL'S. ONE WAS THE ELECTRIC WINDSHIELD HEAT. WINDOW R-2 WAS WRITTEN UP FOR A BURN SPOT ON THE WINDOW. THE PROVISION OF MEL STATES THAT YOU CANNOT FLY INTO KNOWN OR FORECAST ICING. I WANTED TO TALK TO DISPATCH ABOUT THE MEL; BUT GOT SIDETRACKED WITH OTHER ITEMS DURING THE PREFLT AND FORGOT TO CONTACT DISPATCH. THERE WERE SPOTTED STORM IN AZ AND NM AND WX IN THE BNA AREA. MY THOUGHT WAS THAT I COULD AVOID THE WX AREAS IN AZ AND NM; AND THAT THE WX IN THE BNA AREA WAS MOVING E SO THAT IT WOULDN'T BE A FACTOR ON ARR. WE TOOK OFF AND DID DEVIATE AROUND SEVERAL AREAS OF WX. AT 37000 FT; WE WERE ON TOP OF THE WX WITH SLIGHT DEVS TO AVOID WX TOPS. ON ARR INTO BNA; THE WX HAD MOVED OFF TO THE E AND WAS NOT A FACTOR. DURING THIS FLT WE DID AVOID ANY ICING CONDITIONS. HOWEVER; AFTER REVIEWING MEL AND THE DEFINITIONS IN THE MEL; I FEEL THAT THE MEL IS MORE RESTRICTIVE THAN WHAT I INTERPED IT TO BE. AFTER REVIEWING THE MEL; I CAME TO THE CONCLUSION THAT I DID NOT COMPLY WITH THE PROVISIONS STATED IN THE MEL. EVEN THOUGH I AVOIDED ANY ICING CONDITIONS ALONG THE FLT; I DIDN'T COMPLY FULLY WITH THE MEL BECAUSE THERE WAS WX ALONG THE WAY. IF THERE HAD BEEN AN EMER OR OTHER SIT THAT WOULD REQUIRE A DSCNT; THEN WE WOULD HAVE HAD TO DSND INTO THE CLOUDS BELOW US. THANKFULLY THE FLT WAS UNEVENTFUL.