PILOT OF PIPER TURBOPROP REPORTS NMAC AT 6000 FEET WHILE ON VECTORS FOR APPROACH. ONBOARD TRAFFIC ALERT GIVES EARLY WARNING AND EVASIVE ACTION IS TAKEN.

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I WAS BEING VECTORED APPARENTLY DUE TO TFC. APCH HAD ME HDG 340 DEGS OVER LAKE AFTER COMING IN FROM THE E. THE CTLR THEN TOLD ME TO TURN BACK TO A HDG OF 220 DEGS AND CONTACT APCH ON ANOTHER FREQ. I STARTED MY TURN BACK AND SWITCHED TO NEW FREQ WHEN TFC APPEARED ON MY MFD. IT WAS AT THE EXACT SAME ALT AND I WAS HEADING RIGHT FOR IT. I COULD NOT SEE IT VISUALLY. MY TFC WARNING WAS GOING OFF AND I INSTITUTED A DIVING L TURN AS THE MFD HAD AN UP ARROW FOR THIS PLANE. AS IT WENT BY THE MFD SHOWED IT 300 FT ABOVE ME. IT WAS TO MY R ABOUT 200-300 FT. I CONTACTED THE NEW CTLR AND TOLD HIM I HAD JUST HAD TO TAKE EVASIVE ACTION. HE ASKED ME IF THE PREVIOUS CTLR TOLD ME ABOUT THE PLANE AND I TOLD HIM NO. HE ASKED ME IF I GOT AN RA AND I TOLD HIM YES; THINKING HE MEANT A TA (TFC ALERT). AS I DON'T HAVE THE RA CAPABILITY ON MY PLANE (AND DIDN'T KNOW WHAT IT WAS AT THE TIME). I'M SURE THE TAPES WILL CONFIRM ALL THIS. I RE-ESTABLISHED ASSIGNED ALT AND HDG. HE THEN GAVE ME A NEW VECTOR TOWARDS ZZZ AND EVENTUALLY HANDED ME OFF TO ZZZ.