IN-TRAIL SEPARATION REQUIREMENTS LOST AS MLG TOLD TO GAR. CREATES A PROB FOR FLC REGARDING FUEL REQUIRED REMAINING. FUEL EMER DECLARED.

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DISPATCHED OUT OF CLE WITH MINIMUM FUEL; NO ALT (LAX; WX GOOD) -- ENRTE; LAX WX DETERIORATING; DISPATCH GIVES ONT AS ALT. ON APCH; TFC SEPARATION WITH HVY B767 NOT ACCEPTABLE. WE WERE TOLD TO GAR. WE REQUESTED DIRECT TO ONT; DUE TO FUEL SIT. SOCAL APCH ADVISED; HE WOULD HAVE TO TAKE US S OF LONG BEACH AND AROUND TO ONT. WE THEN DECIDED SAFEST ACTION; DECLARE EMER FUEL AND WAS BROUGHT RIGHT INTO LAX; AFTER GAR. SUPPLEMENTAL INFO FROM ACN 343689: WE WERE SCHEDULED TO ARRIVE IN LAX WITH 7500 LBS. ENRTE 2 HRS OUT OF LAX DISPATCH SELCALS OUR FLT; WANTED TO ADD AN ALTERNATE OF ONTARIO; CA; BECAUSE LAX FORECAST HAS CHANGED NOW REQUIRING AN ALTERNATE. MY IMMEDIATE THOUGHT WAS WE DO NOT HAVE ENOUGH FUEL. I EXPRESSED MY CONCERN TO DISPATCH. THEY HAD RUN THE FUEL NUMBERS AND BY THE COMPUTER WE HAD ENOUGH FUEL TO LEGALLY CONTINUE. I TOLD THE DISPATCHER I WOULD NOT CONTINUE BEYOND ONTARIO TO LA IF OUR FUEL STATE WAS LOW. WE WERE HELD DOWN LOW BY ZOB AND; SLOWED PLUS VECTORED BY ZLA. WE WERE RUNNING ABOUT 600 LBS BEHIND APCHING ONTARIO. I DECIDED TO CONTINUE AS APCHS WERE GOING SMOOTHLY. WE WERE SEQUENCED BEHIND A B767 HVY. LAX APCH SLOWED US 4 TIMES; FINALLY REQUESTING APCH SPD. WE NOW HAD 5500 LBS. WE GOT TO THE GATE WITH 4700 LBS. NEVER GO TO A HIGH DENSITY ARPT WITH JUST A LITTLE FUEL. ATC SYS BEING STRETCHED TO BREAKING POINT.