NMAC WHEN AN IFR C172 TRAINING FLT IS ALMOST HIT BY XING TFC AT THEIR ALT 8 MI NW OF FXE; FL.

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AT APPROX XA30 ME AND MY STUDENT JUST FINISHED SHOOTING AN APCH AT BOCA RATON AND WERE BEING VECTORED TO FXE TO SHOOT AN NDB APCH ON AN IFR FLT PLAN. WE HAD BEEN GIVEN SEVERAL TFC RPTS EARLIER THAT DAY. HOWEVER; IT HAD BEEN AT LEAST 5 MINS SINCE OUR LAST TA. MY STUDENT WAS UNDER THE HOOD AND I WAS LOOKING FOR TFC. THE CLOUDS WERE JUST ABOVE US AT APPROX 2100 FT. WE WERE AT 2000 FT MSL. WHEN I LOOKED TO THE L AT APPROX 8 NM NW OF FXE; I SAW A PLANE (C172) APPROX 200 FT JUST OFF MY L WING. I TOOK CTL OF MY PLANE FROM THE STUDENT AND DOVE DOWN TO THE R LOSING APPROX 200 FT OF ALT. I THEN LOOKED FOR THE OTHER PLANE AND SAW HE WAS CLBING AND TURNING TO THE R. I NOTIFIED MIA APCH OF THE SIT AND TOLD HIM I WAS CLBING BACK TO MY ASSIGNED ALT. ALL THE CTLR ASKED ME WAS WHAT TYPE OF ACFT IT WAS. THE CTLR HAD GIVEN ME SEVERAL TA'S DURING THE DAY. IT HAD BEEN AT LEAST 5 MINS SINCE THE LAST ADVISORY. I FEEL IF THE CTLR SEES A SIT (CONFLICT) ON HIS SCOPE; HE SHOULD KEEP AN EYE ON THE SIT UNTIL ONE ACFT SEES THE OTHER. I DO REALIZE CTLRS ARE VERY BUSY AND MAY NOT HAVE TIME TO DO SO. MY OTHER CONCERN IS THAT WE WERE ON AN IFR FLT PLAN AND IN AND OUT OF CLOUDS AT TIMES WHILE AT 2000 FT MSL. IF THE OTHER PLANE AT MY ALT WAS VFR HE WAS SCUD RUNNING; OR IF HE WAS IFR; WHO WAS HE TALKING TO? IT'S SCARY EITHER WAY YOU LOOK AT IT.