A B737-800 DIVERTED TO A NEARBY AIRPORT AFTER DECLARING A LOW FUEL STATE EMERGENCY. THE INTENDED DESTINATION'S RUNWAYS WERE CLOSED FOR AN EMERGENCY AND THE REPORTER'S AIRCRAFT STABILIZER TRIM WAS INOPERATIVE.

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FLT FROM XXX ZZZ1-ZZZ2; ACFT B737-800. RELEASED WITH 19.5 FOB 19.8 BURN 12.9. PLANNED AT FL310 40 MINS HOLD FUEL 3.1. NO ALTERNATE. WX AND FORECASTS GREAT ALONG RTE AND AT DEST. STRONG WESTERLY WINDS DUE A COLD FRONT RECENTLY PASSING THROUGH WAS ONLY NEGATIVE. ENRTE THE ELECTRIC STABILIZER TRIM FROM BOTH PLT POS BECAME INTERMITTENT. THE AUTOPLT WAS ENGAGED AND A FEW MINS LATER WE GOT A STABILIZER OUT OF TRIM LIGHT. THIS LIGHT INDICATES THE AUTOPLT IS UNABLE TO USE ELECTRIC TRIM. WE RAN THE QRH PROC; FLT-C 13/STABILIZER TRIM INOP; THE MANUAL TRIM OPERATED NORMALLY. THE DEST WX DID NOT REQUIRE AN ALTERNATE. CONSIDERING THE DEST WX AND ONBOARD HOLDING FUEL (3100 LBS) I ELECTED TO CONTINUE TO DEST FOR A FLAPS 15 DEG LNDG IN ACCORDANCE WITH THE QRH. BOTH AVAILABLE RUNWAYS MET ALL LNDG REQUIREMENTS. I SENT A CODE FOR OUR MAINT PROB AND SENT A TEXT MESSAGE TO DISPATCH ADVISING OF OUR CONDITION. APCHING THE ARR FIX ABC; 23 MI FROM ZZZ1 ON THE ABC ARR; ATC INSTRUCTED US TO HOLD AT ABC AS PUBLISHED; 8000 FT MSL. ATC RPTED AN ACFT HAD JUST MADE AN EMER LNDG AND TO EXPECT CLRNC FOLLOWING A SHORT DELAY. WE HAD APPROX 5600 LBS ON BOARD. WE ENTERED THE HOLD AND BEGAN PLANNING FOR A DIVERSION ARPT; ZZZ WAS AGREED UPON. AFTER THE AUTHS CLOSED THE DEST ARPT; ZZZ1; I MADE THE DECISION TO DIVERT. I ADVISED ATC OF OUR INTENT TO GO TO ZZZ WITH APPROX 4000 LBS. ATC CLRED US DIRECT ABC1 AND VICTOR AIRWAYS TO ZZZ AT 10000 FT MSL. BEING MINIMUM FUEL AND ABNORMAL CONDITION WE ADVISED ATC THAT WE WERE AT EMER FUEL AND NEEDED TO GO DIRECT ZZZ. THEY CLRED US DIRECT TO THE IAF FOR RWY 28.