AIRBUS A300 FLT CREW HAS A TCAS RA DEP ONT.

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AFTER TKOF; TWR SWITCHED FLT TO SOCAL DEP AND DEP TOLD US TO LEVEL AT 4000 FT DUE TO VFR TFC AT 4500 FT. ACFT LEVELED AT 4000 FT AND STARTED TO ACCELERATE TO 250 KTS. CREW ACQUIRED VISUAL ON CESSNA ACFT AT 4500 FT. DEP GAVE A CLRNC TO CLB TO 14000 FT AND COMPLY WITH SID ALT RESTRS. FO DID NOT HEAR CLRNC CLRLY AND ASKED FOR CONFIRMATION AND CTLR GAVE CLB TO 14000 FT AND DISREGARD ALT RESTRS AND CLRED US DIRECT TO POM VOR. ACFT HAD STARTED A SHALLOW R TURN TO INTERCEPT THE POM 114 DEG RADIAL AND PLT MONITORING DID NOT REDIRECT FMS TO DIRECT POM BECAUSE ACFT WAS TURNING AND WE HAD VISUAL ON TFC. THE TFC WAS FLYING S AND ALTHOUGH IT WAS CLOSER THAN NORMAL; IT WAS NOT GOING TO BE A FACTOR. ONCE OUR ACFT STARTED TO CLB TO 14000 FT THE TCAS RA WARNING WAS ACTIVATED AND COMMANDED A VERT SPD CLB. THE ACFT WAS ALREADY IN THE VERT SPD GREEN BAND WHILE ON THE AUTOPLT AND PROFILE MODE. THE GOOD NEWS IN THIS TCAS EVENT WAS THE CREW HAD A VISUAL ON THE TFC AND WAS CONFIDENT THROUGHOUT THE EPISODE THAT THE TFC WAS NOT GOING TO CREATE A NEAR MISS SITUATION. I BELIEVE THAT IF THE CTLR HAD ALLOWED US TO CLB TO 7000 FT AFTER TKOF; WE WOULD HAVE AVOIDED ANY TCAS CONFLICT WITH THE VFR TFC AT 4500 FT.