AN IFR CE525 PILOT DEPARTING DAL HAD A NEAR MISS TCAS EVENT AFTER MISTAKING AN ALT CLEARANCE AND CLBING TO 12000 FT WHEN CLEARED TO 10000 FT.

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DEPARTED DAL WITH AN IFR CLRNC FOR RADAR VECTORS FOR THE JOE POOL.3 DEP. ON CLBOUT; RECEIVED INSTRUCTION FOR IMMEDIATE EVASIVE ACTION; 'TURN TO HDG 270 DEGS.' SECONDS LATER; RECEIVED AURAL AND VISUAL WARNING OF 'TFC' FROM ONBOARD TCAS. CTLR ADVISED THAT I HAD ONLY BEEN CLRED TO 10000 FT MSL AND HAD CREATED A 'NEAR MISS' AS I CLBED THROUGH 110000 FT MSL. I THOUGHT I HAD BEEN CLRED TO 12000 FT MSL; AND UPON HIS WARNING VERIFIED THAT I HAD WRITTEN DOWN AND ENTERED 12000 FT IN THE ALT PRE-SELECTOR. CTLR MAINTAINED THAT ANOTHER ACFT HAD BEEN CLRED TO 12000 FT AND THAT THEY HAD ACKNOWLEDGED THE CLRNC. I WOULD LIKE TO HEAR THE AUDIO RECORDING OF THE CLRNC AND ACKNOWLEDGEMENT XMISSIONS AS I REALLY HAD NO DOUBT ABOUT BEING CLRED TO 12000 FT. IF I WAS IN FACT ONLY CLRED TO 10000 FT AND ACKNOWLEDGED SUCH; THEN MY BRAIN WAS COMPLETELY DISCONNECTED. I HAVE HAD TIMES WHEN I WAS DAYDREAMING OR UNSURE OF A CLRNC FOR WHATEVER REASON; BUT THIS WAS NOT ONE OF THEM. NEVERTHELESS; IN HINDSIGHT THE ONE THING I REALIZE I SHOULD HAVE DONE BETTER IS MONITORING THE TCAS DISPLAY. RECEIVING A TFC WARNING SHOULDN'T BE A SURPRISE IF YOU ARE APPROPRIATELY MONITORING THE MOVEMENT OF TARGETS; WHICH I WAS NOT. EVEN IF I WAS CLRED TO 12000 FT; SEEING THE APCHING TFC WOULD HAVE CAUSED ME TO QUESTION THE CTLR THUS POINTING OUT OUR DIFFERENCE OF UNDERSTANDING AND ALLOWING A MORE TIMELY CORRECTION OF THE SITUATION. WE ARE THE BENEFICIARIES OF A NUMBER OF EXTRAORDINARY PIECES OF TECHNOLOGY; BUT THEY ARE ONLY BENEFICIAL TO THE EXTENT WE UTILIZE THEM.