DURING CLB OFF PHX; A B737 CREW RECEIVES A TCASII TA ON TFC 800 FT ABOVE THEIR ALT.

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WE WERE DEPARTING PHX ON RWY 7R; CLRED VIA THE SILOW ONE DEP TO OUR ASSIGNED ALT OF 7000 FT. CAPT WAS THE PF. THE FO SWITCHED TO DEP CTL AND ADVISED HIM WE WOULD BE REQUIRING VECTORS FOR TSTMS TO THE NE OF THE ARPT. DEP ASSIGNED US A HEADING OF 020 DEGS. AFTER WE LEVELED AT 7000 FT; DEP ASKED US AREN'T YOU CLBING TO FL210? THE FO RESPONDED CLBING TO FL210. WE THEN RESET OUR ALT SELECTOR TO FL210 AND PROCEEDED TO CLB. DEP CTL THEN TURNED US R TO A HEADING OF 060 DEGS. THE CTLR ASKED US IF WE HAD A B727 IN SIGHT. WE DID NOT SEE THE ACFT. THE FO OBSERVED TCASII TARGET 800 FT ABOVE US. THERE WAS NO RA. THE CTLR TURNED US FURTHER R TO 090 DEGS. THE CTLR THEN GAVE US A L TURN DIRECT TO THOMM INTXN; WHICH IS ON THE SILOW ONE DEP. UPON LNDG AT PORTLAND; GND CTL GAVE US A PHONE NUMBER AND WANTED US TO CONTACT THEM. I SPOKE WITH THE PHOENIX DEP SUPVR. HE SAID HE WAS LOOKING INTO A POTENTIAL VIOLATION. WE WERE UNAWARE WE HAD VIOLATED ANY RULES. HE INFORMED ME THAT WE HAD MISSED AN ASSIGNED ALT. HE ASKED ME TO CALL HIM BACK SEVERAL HRS LATER; WHICH I DID. HE SAID THAT HE HAD LISTENED TO THE AUDIO TAPE AND THAT OUR FLT HAD ACKNOWLEDGED AN ALT ASSIGNMENT TO FL210 AT OUR INITIAL CHK-IN CALL. THE FO AND I HAVE NO RECOLLECTION OF THE FL210 ASSIGNMENT UNTIL THE SECOND CALL FROM THE CTLR. JUST PRIOR TO DEP; WE RECEIVED AN ACARS MESSAGE FROM DISPATCH RPTING TSTM WITH 5 MI OF THE FIELD. BOTH OF US WERE INTENT ON AVOIDING RADAR RETURNS THAT WERE ON OUR DISPLAY. IT IS POSSIBLE THAT WE UNINTENTIONALLY MISSED THE CALL AND MAY HAVE EVEN READ IT BACK. WE DID NOT SET FL210 ON THE ALT WINDOW AT THAT TIME.