B757 FLT CREW DEPARTED ON RWY THAT IS NOT AUTHORIZED FOR CURRENT WX MINIMUMS.

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I GOT OUR FLT DEP PAPERS AND WENT OVER THEM WITH THE FO. I NOTICED THAT THE DEP VISIBILITY WAS 1/8 MI. WE HAD DISCUSSED LOW VISIBILITY ON THE INBOUND FLT AND WITH OTHER CREWS AND DETERMINED THAT WE COULD DEPART WITH 600 FT RVR OR 1/16 MI VISIBILITY. I GOT A TKOF ALT FROM DISPATCH; WHILE THE FO FINISHED WITH THE PAPERWORK. AFTER ARRIVING AT THE ACFT; WE LISTENED TO THE ATIS AND SAW THAT THE VISIBILITY HAD GONE DOWN TO 1/16 MI; BUT WE WERE OK WITH THAT; AS THE RWY WAS RATED FOR THAT. I CHKED THE CHART FOR THE ARPT AND SAW THAT THE LOW VISIBILITY TXWY WAS GOOD FOR THE ENTIRE LENGTH OF RWY 7/25 IN BOTH DIRECTIONS. DURING TAXI OUT THE FO ASKED IF HE SHOULD REQUEST RWY 25 AS HE NORMALLY DOES; AS THAT IS THE MOST DIRECT DIRECTION FOR OUR DEP; AND I SAID 'SURE' AS I USUALLY DO. THE GND CTLR THEN CLRED US TO RWY 25; AND AFTER TAXI OUT CLRED US FOR TKOF ON RWY 25. I MADE THE TKOF AS REQUIRED AND IT WAS NORMAL; AS WAS THE CLB TO ALT. HOWEVER; AT LEVELOFF; FOR SOME REASON; I DECIDED TO RECHK THE TKOF RWY'S VISIBILITY REQUIREMENT; AND FOUND THAT RWY 7; NOT RWY 25 HAD THE 1/16 MI APPROVAL. I INFORMED THE FO AND WE BOTH CHKED AND VERIFIED THIS. SUPPLEMENTAL INFO FROM ACN 696168: WHEN DOING PREDEP PAPERWORK WE DISCUSSED THE LOW VISIBILITY TKOF. THE CAPT LOOKED UP THE RWY INFO FOR RWY 7 WHICH WAS IN USE. WX WAS WITHIN LIMITS AND WE FINISHED THE PAPERWORK; WENT TO THE ACFT AND STARTED ENGS. WE DISCUSSED USING RWY 25 FOR DEP BECAUSE IT HEADED US TOWARD OUR DEST.