A B737-800 ON APCH TO DFW EXPERIENCED A CONFLICT WITH A DEP FROM A XING RWY.

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ON FINAL TO RWY 17L AT DFW INSIDE THE FAF WE HEARD A FLT CLRED FOR TKOF ON RWY 13L. WE WERE IMC AT THIS TIME. WE BROKE OUT AT ABOUT 1000 FT AND THE FO STARTED LOOKING FOR THIS FLT. IT TOOK AWHILE BECAUSE HE EXPECTED THE FLT TO BE IN THE AIR OR NEAR THERE. IT WAS IN FACT JUST BEGINNING HIS ROLL. HE CALLED IT IN SIGHT AND SAID IT WAS GOING TO BE CLOSE. I LOOKED FOR THE PLANE AND HAD THE SAME PROB; EXPECTING IT TO BE FARTHER ALONG. WE CONTINUED AND THE ACFT LIFTED OFF AND CLBED OUT RIGHT THROUGH OUR FLT PATH (THE ACFT ACTUALLY WENT THROUGH THE FLT PATH VECTOR ON THE HUD). WE WERE APPROX 1/2 MI FROM IT AT THIS POINT. IT CLRED AND WE CONTINUED AND LANDED NORMAL. I'M NOT SURE IF THIS MEETS THE CRITERIA FOR A NEAR MISS. AT THE LEAST IT WOULD HAVE BEEN VERY DISCONCERTING TO HAVE BEEN AT THE CLOSEST POINT AND JUST POPPING OUT TO THE CLOUDS AND HAVE A PLANE 'BORESIGHTED' IN THE HUD. THE FO'S SITUATIONAL AWARENESS WAS SUPERB AND HELPED ME IMMENSELY WITH THIS SITUATION. AS I SAID I DON'T THINK THERE WAS MUCH RISK OF COLLISION SINCE OUR COURSES WERE SO DIVERGENT; BUT IT WAS STILL A LITTLE UNCOMFORTABLE.