B737-800 EXPERIENCES TCASII RA DSNDING INTO DFW. CTLR CLAIMS AMENDED CLRNC GIVEN; BUT FLT CREW DO NOT HEAR OR ACKNOWLEDGE IT.

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I AM A B737 CHK AIRMAN AND HAD DISPLACED THE FO FOR THE FLT. WHILE DSNDING INTO DFW AND CLRED TO 11000 FT; WE WERE GIVEN HOLDING AT CQY APPROX 15 MI PRIOR TO THE FIX. THIS WAS DUE TO A CHANGE OF LNDG DIRECTION AT DFW. THE CTLR HAD ASKED US TO EXPEDITE DSCNT THROUGH FL200. AT APPROX FL210 IN OUR EXPEDITED DSCNT; I NOTICED ON THE TCASII AN ACFT AHEAD AND TO THE L (AMBER). WE WERE BEGINNING OUR TURN IN HOLDING AT THE SAME TIME; AND I SAW HIM AHEAD AND BELOW US AT FL190. AT THE SAME TIME; WE HAD A TCASII A TO STOP OUR DSCNT; WHICH I DID AT FL203. WE NOTIFIED ATC OF THE RA; AND ASKED ABOUT OUR CLRNC TO 11000 FT. HE SAID HE THOUGHT HE HAD GIVEN US AN AMENDED CLRNC FOR FL200. WE DID NOT HEAR THAT CLRNC. THE CTLR WAS VERY BUSY BECAUSE OF THE CHANGE OF RWYS AT DFW AND GAVE US THE HOLDING CLRNC WITH VERY SHORT NOTICE. AT NO TIME WAS THERE A SEPARATION CONFLICT AS WE STOPPED OUR DSCNT AND MAINTAINED FL200. ONCE AGAIN; TCASII HAS PROVEN ITSELF AN INVALUABLE TOOL IN THE COCKPIT. SUPPLEMENTAL INFO FROM ACN 630121: SEPARATION IN DISTANCE AT FIRST SIGHTING: 2000 FT. PROX AT CLOSEST POINT HORIZLY AND VERTLY: 500 FT/800 FT. DEGREE OF EVASIVE ACTION: LEVELED AND CLBED TO FL200. NO INJURIES.