A B737-200 FLT HAS AN NMAC WITH A LIGHT TWIN CESSNA VFR AT 17500 FT WHILE ON THE TEXOMA 7 DEP FROM DFW; TX.

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WE WERE CLBING OUT OF DALLAS ON THE TEXOMA 7 DEP. WE RECEIVED A COUPLE OF HDGS TO INTERCEPT THE RANGER (FUZ) 360 DEG RADIAL FROM ZFW. OUR INITIAL CLB CLRNC WAS TO 12000 FT -- WE RECEIVED A FURTHER CLRNC TO CLB TO FL220. WE WERE WELL ESTABLISHED IN THE CLB WHEN I NOTICED A TCASII TARGET APPEAR ON THE TCASII VSI. I COULD SEE FROM THE TARGET MOVEMENT ACROSS THE SCREEN AND ALT ABOVE US THAT WE WERE CONVERGING QUICKLY. VERY QUICKLY WE RECEIVED A TA FOLLOWED BY AN RA WHICH COMMANDED A DSCNT. OUR -200 WAS CLBING AT ABOUT 200 FPM. I PULLED THE THRUST LEVERS BACK AND BEGAN TO PUSH THE NOSE OVER TO ESTABLISH A DSCNT. AS THIS HAPPENED; THE CONFLICT ACFT PASSED OVERHEAD; THE TCASII VSI INDICATED HE WAS 500 FT ABOVE US. HE NEVER ALTERED HIS COURSE OR APPEARED TO CHANGE ALT. ZFW NEVER SAID ANYTHING ABOUT THIS TFC. WE INFORMED ZFW THAT WE WERE EXECUTING AN RA FOR TFC CONFLICT. THE CTLR ROGERED OUR CALL; AGAIN WITH NO EXPLANATION. A COUPLE OF MINS WENT BY AND ZFW CAME BACK AND RECLRED US TO FL220. THE CTLR SAID OUR CONFLICT ACFT (A CESSNA TWIN) WAS A VFR ACFT AT 17500 FT; HE WAS NOT TALKING TO ANYBODY. THE ACFT OBVIOUSLY HAD A XPONDER BECAUSE OUR TCASII INTERCEPTED IT AND ZFW WAS TRACKING IT. ZFW SHOULD HAVE GIVEN US MORE WARNING; CHANGED OUR HDG OR CAPPED OUR ALT TO AVOID THIS CONFLICT. THE TCASII SYS WAS INVALUABLE TO US PREVENTING A CONFLICT. SUPPLEMENTAL INFO FROM ACN 556938: WE WERE CLBING THROUGH 16500 FT AT 2000 FPM; WHEN WE RECEIVED A TCASII ALERT. AT APPROX 17000 FT; WE RECEIVED A TCASII RESOLUTION TO DSND. THE CONFLICT ALERT WAS PICKED UP VISUALLY AT APPROX 1 MI HORIZ DISTANCE. I TOLD ATC THAT WE WERE DSNDING TO COMPLY WITH OUR TCASII RA. THE CTLR RESPONSE WAS 'ALL I CAN SAY IS ROGER' FOLLOWED BY 'THERE IS VFR TFC AT 17500 FT.' IF WE HAD NOT HAD TCASII WHICH ALLOWED US TO SEE THE ACFT VISUALLY; THIS WOULD HAVE BEEN MUCH CLOSER. THIS EVENT OCCURRED AT A CRITICAL ALT DUE TO BOTH PLTS LOOKING INSIDE TO SET ALTIMETERS TO 29.92 TO TRANSITION TO THE FLT LEVELS. IT WOULD HAVE BEEN MOST HELPFUL IF THE CTLR WOULD HAVE ISSUED TFC TO US.