A DEP CRJ200 AND A XING C182 HAVE AN NMAC IN CLASS C AIRSPACE E OF FLL; FL.

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ON THE CLBOUT AFTER TKOF AND GOING THROUGH 1000 FT MSL; WE RECEIVED A TA. WITHIN A FEW SECONDS; IT WAS FOLLOWED BY AN RA. WE ALL ESTABLISHED VISUAL CONTACT WITH THE SMALL GA ACFT WHICH WAS WITHIN 1/4 MI AT 12 O'CLOCK POS. DUE TO FOLLOWING THE RA PROC AND THE CLB PERFORMANCE OF THE RJ; WE ARRANGED TO CLB OVER THE TOP OF THE GA ACFT. JUST ABOUT THIS TIME; WE RECEIVED THE TA FROM THE TWR AND WE WERE TOLD THAT THE TFC HAD JUST POPPED UP ON THEIR RADAR SCREEN. I CONTACTED THE TWR UPON ARR AT DCA AND WAS TOLD THAT THE GA ACFT WAS NOT IN COM WITH FLL; BUT THEY MANAGED TO GET IN TOUCH WITH THEM A FEW MINS LATER AND WERE TOLD THAT GA ACFT SAW US AND HE WAS AT 1500 FT AND DSNDED TO AVOID COLLISION WITH US. HE WAS ALSO VERY APOLOGETIC. THE FLL TWR TOLD ME THAT THEY WERE FORWARDING A RPT TO WASHINGTON ABOUT THE ALTDEV. I AM NOT SURE HOW QUICKLY THE TWR SAW THE TFC ON RADAR AS IT SEEMS THAT THEY HAD MISSED IT. THEY HAD ALSO NEVER INFORMED US OF HELI TFC THAT WAS 300 FT BELOW US ON THE ARR TO FLL JUST ABOUT 45 MINS PRIOR TO THIS INCIDENT. SUPPLEMENTAL INFO FROM ACN 617527: DEPARTING E ON RWY HDG RECEIVED RA; 'CLB.' 'MAINTAIN VERT SPD;' THEN 'CLR OF CONFLICT.' SUBSEQUENTLY SPOKE WITH ATC WHO SAID THEY 'NEVER SAW HIM; HE WAS A FOREIGN STUDENT PLT OVERFLYING THE INTER-COASTAL WATERWAY AT 1500 FT.' TWR DID NOT ADVISE OF HELI TFC WHICH FLEW DIRECTLY BENEATH US 500 FT BELOW. LUCKILY; WE SAW THAT TFC AND REMAINED ABOVE GS IN RESPONSE TO A 'TFC;' TA RECEIVED BY TCASII. ONE THING IS CERTAIN; TCASII WORKS! DEFINITELY SAVED OUR LIVES THAT DAY! I THINK FLL NEEDS SOME NEW EQUIP OR TRAINING.