B737 FLT CREW DEPARTING LAS ON VECTORS; RECEIVED CONFLICTING INSTRUCTIONS FROM ATC WITH REGARDS TO CONFLICT AIRCRAFT ON TCAS.

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I WAS THE FO ON FLT FROM LAS. WE DEPARTED RWY 1R ON ATC VECTORS. THE CAPT PERFORMED THE TKOF AND CLBING THROUGH 5000 FT HE TRANSFERRED CTLS OVER TO ME. OUR INITIAL CLRNC WAS A W HDG FROM LAS DEP FOLLOWED BY A 210 DEG HDG AND CLRNC TO 12000 FT. THE CAPT RESPONDED 12000 FT TO ATC. WE WERE IN IMC CONDITIONS FROM ABOUT 7000 FT AND DURING THE WHOLE EVENT. CLBING THROUGH 10000 FT; WE COMPLETED THE CLB CHKLIST. SHORTLY AFTER CLBING THROUGH 11000 FT LAS DEP GAVE US INSTRUCTIONS TO DSND TO 10000 FT. ATC RESPONDED AGAIN WITH URGENCY TO DSND TO 10000 FT. OUR CLB RATE WAS ABOUT 2000 FPM AND I STARTED TO REVERSE THE VERT DIRECTION OF THE AIRPLANE. ATC THEN GAVE US A NEW HDG OF 240 DEGS WITH URGENCY TO AVOID TFC. THE CAPT RESUMED CTL OF THE ACFT AT THIS POINT AND KEPT THE ACFT CLBING TO AVOID TFC THAT WAS BTWN 500-1000 FT BELOW US. WE RECEIVED A TFC ALERT FROM OUR TCAS SYS; HOWEVER; DID NOT RECEIVE AN RA. WE RESPONDED THAT WE WERE ON A 240 DEG HDG TO ATC AND THE CAPT KEPT THE ACFT CLBING TO ABOVE 12300 FT. WHEN WE WERE CLR OF TFC; LAS DEP GAVE US CLRNC TO CLB TO 19000 FT AND DIRECT TO A FIX TO RESUME THE DEP. I THINK THAT ATC WAS NOT AWARE THAT INSTRUCTING US TO CLB TO 12000 FT ON OUR 210 DEG HDG WAS GOING TO PUT US IN CONFLICT WITH ANOTHER ACFT. AT THE POINT ATC TOLD US TO DSND; THE CTLR WOULD HAVE HAD US DSNDING BACK TOWARDS THE OTHER ACFT. BETTER AWARENESS FROM ATC BOTH DIRECTIONALLY AND VERTLY TO AVOID TFC COLLISIONS IN THE LAS VEGAS DEP. I ALSO THINK THAT WHEN THIS HAPPENS THE CREW NEEDS TO IMMEDIATELY TURN OFF THE AUTOPLT AND HAND FLY THE AIRPLANE FOR BETTER RESPONSE TIME TO AVOID TFC. SUPPLEMENTAL INFO FROM ACN 807785: AS WE ROLLED OUT ON HDG; I WAS ABLE TO GET THE NOSE DOWN AND STARTED THE DSCNT. ATC THEN DIRECTED TO AGAIN MAINTAIN 12000 FT. AS MUCH AS I LIKE GETTING OUT OF LAS; IF WE HAD FLOWN THE SID IN ITS ENTIRETY; NOTHING MAY HAVE HAPPENED. IF WE DID RECEIVE A BAD ALT CLRNC (WE BOTH HEARD 12000 FT) NOTHING WOULD HELP. THE CTLR WAS VERY BUSY.