A CPR FLC OF AN MDT GETS AN RA AND AVOIDS A LIGHT TWIN ACFT THAT CLBS THROUGH THEIR ALT WITHOUT TALKING TO MIA APCH CTL. THE APCH CTLR SAID THAT HE WAS NOT AWARE OF THE CONFLICTING ACFT.

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WE WERE FLYING THE MRLIN 4 ARR TO FLL; LEVEL AT 6000 FT PER MIA APCH CLRNC BTWN TRITN AND WISCI INTXNS. TCASII DISPLAYED A TA AT OUR 12 O'CLOCK POS AT ABOUT 4 MI 300 FT BELOW AND CLBING. THE TA THEN WENT TO AN RA WITH ADVISORY TO CLB WITH THE GREEN FLY TO AREA ON IVSI AT 3000 FPM. THE RA WAS FOLLOWED AND ATC WAS ADVISED THAT ASSIGNED ALT WAS VACATED BASED ON A TCASII CLB ADVISORY. MAX ALT DURING THE RA EVENT WAS 900 FT ABOVE ASSIGNED ALT. THE TFC WAS SEEN PASSING UNDER OUR ACFT 600 FT BELOW; ON NEAR R SIDE. WHEN CLR OF CONFLICT; WE RETURNED TO ASSIGNED ALT OF 6000 FT AND ADVISED ATC. THE TFC CONTINUED TO CLB AS IT WENT OFF TCASII DISPLAY BEHIND US. WHEN ATC WAS QUESTIONED ABOUT THE TFC THEY INDICATED THAT THEY WERE NOT TALKING TO THE ACFT AND WAS NOT AWARE OF THE TFC. AT 6000 FT WE WERE JUST ON TOP OF BROKEN CLOUDS. THE CONFLICTING TFC WAS A LIGHT TWIN AND WAS NOT SEEN UNTIL IT PASSED UNDER OUR ACFT DURING THE RA CLB. I WAS THE CAPT IN CHARGE OF THE TRIP AND WAS IN R SEAT DURING THAT LEG OF TRIP. IN MY OPINION THE TCASII SAVED A POTENTIAL MIDAIR OR AT THE VERY LEAST A VERY NEAR MISS AS THE OTHER ACFT WOULD NOT HAVE BEEN SEEN CLBING THROUGH THE BROKEN CLOUDS.