MLG HAS TCASII RA. HAD TFC IN SIGHT BUT CLBED.

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ON 'BLUE RIDGE 3 ARR' INTO DFW WE HAD A TCASII RA TO CLB 1000-1500 FPM. WE WERE LEVEL AT 11000 FT AND SLOWING FROM 250-210 KTS AS WE APCHED THE HAMAK INTXN. WE HAD NOT BEEN GIVEN A TA BY ATC; HOWEVER; I HAD VISUAL WITH AN MLG ACFT; CLBING OUT FROM DFW ABOVE AN UNDERCAST. IT WAS AT 2 O'CLOCK AND AS WE APCHED THE TFC IT BEGAN TO MOVE AFT ON THE WIND SCREEN. FROM MY PERSPECTIVE; THE TFC WAS NOT A THREAT. AS THE TFC PASSED 3 O'CLOCK; TCASII GAVE US A CLB COMMAND. IT SHOWED TFC AT APPROX 1 MI; 3 O'CLOCK; 900 FT BELOW AND CLBING. I VISUALLY CONFIRMED THE TFC'S POS AS WE INITIATED THE CLB. THE CAPT FELT WE SHOULD FOLLOW THE COMMANDS TO BE ON THE SAFE SIDE. WE FOLLOWED THE TCASII INSTRUCTIONS UNTIL WE WERE GIVEN THE 'CLR OF TFC' CALL THEN WE DSNDED AND FOLLOWED ATC'S NEW INSTRUCTIONS. DURING THE TCASII ALERT WE HAD TO IGNORE ALT; HDG; AND AIRSPD RESTRICTIONS GIVEN ALMOST SIMULTANEOUSLY WITH THE TCASII COMMANDS. ALTHOUGH THE TFC HAD BEEN A FACTOR; NEITHER THE CAPT NOR I THOUGHT IT WAS A THREAT. AFTER LNDG A TRACON SUPVR ASSURED US THAT THE TFC WAS LEVEL 1000 FT BELOW US AND THAT IT PASSED BEHIND US.