TCASII RA FLOWN IN DFW CLASS B AIRSPACE. ATC RPTED INTRUDER AS POP UP TFC.

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DEPARTED RWY 18R AT DFW. MADE R TURN TO 240 DEG HDG AND WAS CLBING TO 2000 FT AS PER THE DEP CLRNC. HANDED OFF TO DEP CTLR. TOLD TO FLY HDG 270 DEGS AND CLB TO 4000 FT. PASSING THROUGH 3600 FT; RECEIVED TCASII WARNING (RA) TO DSND. I (THE FO AND PF) IMMEDIATELY BEGAN A DSCNT. AT THE SAME TIME THE CAPT (PNF) LOOKED TO VISUALLY ACQUIRE THE ACFT AND TELL THE CTLR WHAT WE WERE DOING. THE CTLR TOLD US TO DSND TO 2000 FT. THE CAPT ACKNOWLEDGED THE CLRNC AND TOLD THE CTLR WHAT WE WERE DOING. THE CTLR THEN STATED THAT THE ACFT CAME OUT OF NOWHERE AND HAD MADE A TURN TOWARDS THE S AT US. BY THIS TIME THE CAPT HAD A VISUAL ON THE ACFT AND POINTED IT OUT TO ME. I COULD TELL IT WAS A SINGLE-ENG; LOW WING RETRACTABLE GEAR BUT NOT WHAT MAKE IT WAS. I ALSO KNEW MY ACTIONS ON THE CTLS WERE GOOD AND WE WOULD CLR THE OTHER ACFT. BY THE TIME I LEVELED OUR PLANE; THE OTHER ACFT WAS GONE. THE CAPT SAID SHE THOUGHT THE OTHER ACFT PASSED APPROX 200 FT ABOVE US AND 300-500 FT BEHIND US. I COULDN'T SAY -- I JUST KNEW WE WOULD CLR THE OTHER ACFT. THE CAPT QUERIED THE CTLR ABOUT THE OTHER ACFT; AND SHE AGAIN STATED THE ACFT JUST POPPED UP AND TURNED TOWARDS US. SHE THEN GAVE US A NEW HDG AND ALT TO CLB TO; AND THAT WAS ALL THAT WAS SAID. THE CAPT AND I BOTH AGREED WITH THAT; AS WE NEVER GOT THAT CLOSE . ALERTS: EVEN WHEN THE TCASII GOES TO A DARKER COLOR; THERE IS TIME TO LOOK BEFORE THE COMPUTER TELLS YOU A COMMAND. THIS ONE WAS SIMULTANEOUS. WE ALSO AGREED THAT WE AND THE CTLR DID ALL WE COULD UNDER THE CIRCUMSTANCES. THANK GOODNESS FOR THE TCASII. IT DID ITS JOB THIS TIME.