FLC OF AN MLG TOOK EVASIVE ACTION BY DSNDING FROM ASSIGNED APCH ALT IN RESPONSE TO TCASII RA.

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LEVEL AT 6000 FT MSL ON A VECTOR TO BASE LEG. ATC CALLED TFC AT 2 O'CLOCK (I THINK) AT 5500 FT. WE HAD HIM ON TCASII AT -500 FT AT 2 O'CLOCK. FO CALLED TFC IN SIGHT. ABOUT 10-15 SECONDS LATER WE GOT RA TO DSND; DSND NOW XING TFC. I REACTED IMMEDIATELY AND AGGRESSIVELY DSNDED TO 4000 FT MSL. TCASII WAS SCREAMING THE WHOLE TIME. IVSI WAS ALL RED WITH ABOUT 1/4 INCH GREEN AT THE BOTTOM. LEVEL AT 4000 FT MSL. I ASKED THE CTLR WHAT HAD HAPPENED. HE SAID THE ACFT THAT WE CALLED IN SIGHT HAD CLBED INTO US AND HE HAD HIM AT 5800 FT. HE SAW US REACT TO RA AND I ASKED HIM IF HE WAS SURE IT WAS THE SAME ACFT HE CALLED EARLIER BECAUSE HE SEEMED TO COME OUT OF NOWHERE. HE SAID IT WAS. WE CALLED HIM ON THE GND. HE SAID THE INTRUDER ACFT WAS IN CLASS B AIRSPACE AND NOT TALKING TO ANYONE. IT WOULD HAVE BEEN NICE TO HAVE HAD THIS INFO WHEN HE CALLED THE TFC AT 5500 FT EARLIER. I ASSUMED THE GUY WAS ASSIGNED 5500 FT. I ASKED HIM WHERE THE GUY WENT AND HE SAID HE DIDN'T KNOW. I SUSPECT HE LANDED AT ONE OF THE LCL SMALL ARPTS. THIS WAS CLOSE -- VERY CLOSE. TCASII WORKED -- DON'T LEAVE HOME WITHOUT IT. THIS IS THE SECOND EVENT THAT I KNOW OF THIS YR BTWN MY AIRLINE AND A SMALLER ACFT. TCASII SAVED US BOTH.