A319 CREW HAD NMAC WITH VFR ACFT.

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WE DEPARTED PIT USING RWY 28R AND HAD BEEN GIVEN AN EBOUND HDG FROM DEP CTL AND TO CLB TO 14000 FT. DUE TO TSTM ACTIVITY; WE REQUESTED A TURN HDG S; BUT WERE APPROVED TO DEVIATE EITHER E OR N. WE CHOSE TO DEVIATE AROUND THE TSTMS ON AN EASTERLY HDG. AT APPROX 12000 FT MSL; WE RECEIVED A TCASII ADVISORY WITH THE INTRUDER BEING IN FRONT OF US AND 800 FT HIGHER. AT APPROX 12500 FT; WE GOT AN RA AND DISCONNECTED THE AUTOPLT AND BEGAN AN IMMEDIATE ABRUPT PITCH DOWN TO DSND. ACCORDING TO THE TCASII; WE CAME WITHIN 200 FT OF EACH OTHER. WE NEVER SAW THE INTRUDER BECAUSE WE WERE IMC AT THE TIME. WE THEN RECEIVED OUR 'CLR OF CONFLICT' (APPROX 11000 FT) AND CONTINUED OUR CLB TO 14000 FT. THE REST OF THE TRIP WAS NORMAL. WE ASKED DEP WHY WE WERE NEVER MADE AWARE OF THE TFC AND WERE TOLD THAT THE TFC WAS VFR AND THAT IT DID NOT HAVE TO BE RPTED. THE CTLR WAS EXTREMELY BUSY AT THE TIME (DUE TO THE TSTMS). MY THOUGHT ABOUT THIS IS THAT TCASII DID ITS JOB VERY WELL. I LEARNED THAT YOU MUST BE FULLY AWARE OF A TA AND READY TO REACT TO AN RA. GND SCHOOL AND SIMULATOR EDUCATION OF TCASII IS ESSENTIAL FOR THIS. I BELIEVE THAT THE TCASII IN THIS SIT POSSIBLY PREVENTED A MAJOR CATASTROPHE.