A B737-700 DEPARTING LAS RWY 19L ON THE TRALR 1 FOLLOWING A PREVIOUS RWY 19R DEP RECEIVED AN RA FROM AN UNKNOWN RWY 19R FOLLOWING ACFT.

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WE WERE CLRED FOR TKOF ON RWY 19L IN LAS FOR THE TRALR DEP. WHEN WE WERE CLRED FOR TKOF; WE WERE TOLD TO MAINTAIN VISUAL SEPARATION WITH A CITATION X WHO WAS JUST ROTATING OFF OF RWY 19R. WE FLEW THE DEP AS PER COMPANY SOP AND AT FIXIX THE AUTOPLT INITIATED A TURN TOWARDS ROPPR. AT THAT MOMENT WE RECEIVED A TCASII RA TO DSND. THE VVI COMMANDED A DSCNT IN EXCESS OF 2500 FPM. I DISCONNECTED THE AUTOPLT AND CONTINUED IN THE TURN WHILE DSNDING TO MEET THE RA DSCNT REQUIREMENT. THE CAPT TOLD ATC THAT WE HAD AN RA BUT I DON'T THINK THE CTLR HEARD IT AS THE FREQ WAS EXTREMELY BUSY. WE WERE AT ABOUT 6200 FT WHEN WE GOT THE RA AND RECOVERED AT ABOUT 5000 FT. WHEN WE GOT THE 'CLR OF CONFLICT' WE CONTINUED THE CLB BUT WERE INSTRUCTED TO CLB TO FL190 AND TURN DIRECT TO WILLW INTXN. I INITIATED THE TURN AND THE CLB AND A GULFSTREAM WAS IMMEDIATELY TO OUR L AND VERY CLOSE. IF I HAD CONTINUED THE TURN; I WOULD HAVE PROBABLY GOTTEN VERY CLOSE TO HIM. PUT IT THIS WAY; THE GULFSTREAM WAS WHITE WITH A SMALL COLORED STRIPE AND COLORED TAIL. AT THAT TIME WE RECEIVED A TCASII TA ABOUT THE SAME TIME. I IMMEDIATELY STOPPED THE TURN AND INITIATED A STEEPER CLB TO TRY TO GET AWAY FROM HIM. THE CAPT AND I HAVE NO IDEA WHERE THE GULFSTREAM CAME FROM. I INITIALLY THOUGHT THAT THE RA WAS BECAUSE OF THE CITATION X THAT WE HAD IN SIGHT. LUCKILY; I STILL COMPLIED WITH THE RA BECAUSE IT WAS FOR A SECOND ACFT. I BELIEVE THAT WHEN WE GOT THE INITIAL RA; THE GULFSTREAM WAS ABOVE ME AND TO MY R (AS IF HE HAD TAKEN OFF ON RWY 19R). BY THE TIME I WAS DONE COMPLYING WITH THE RA; HE ENDED UP ON THE L SIDE OF ME AND ABOVE ME (BECAUSE OF THE TURN TOWARDS ROPPR). I WOULD REALLY LIKE TO KNOW WHERE THE GULFSTREAM CAME FROM. I WOULD ASSUME THAT HE TOOK OFF FROM RWY 19R AND WAS TOLD TO MAINTAIN VISUAL SEPARATION WITH US. WE WERE MARGINALLY HVY AND CLBING SLOW SO HE MUST HAVE OVERTAKEN US. NONETHELESS HE SHOULDN'T HAVE GOTTEN SO CLOSE. WE NEVER HEARD ANY KIND OF TFC WARNING FROM ATC AND HE WAS RIGHT ON TOP OF US. I CANNOT EMPHASIZE ENOUGH THAT WHEN YOU GET AN RA; COMPLY WITH IT! HAD I ASSUMED THE CITATION X WAS THE ACFT IN QUESTION; I COULD HAVE BEEN DEADLY WRONG. TCASII IS A WONDERFUL THING! DON'T LEAVE HOME WITHOUT IT! I DON'T KNOW IF THERE IS ANY WAY TO FIND OUT MORE INFO ABOUT THIS INCIDENT; BUT I SURE WOULD LIKE TO KNOW WHERE THE GULFSTREAM CAME FROM; AND WHY ATC NEVER TOLD US ABOUT HIM.