A320 BEGINS TO TAXI PRIOR TO RECEIVING A CLRNC FROM THE RAMP PUSHBACK CREW AT ORD.

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WE PUSHED BACK FROM GATE X AT ORD 15 MINS LATE DUE TO A LATE INBOUND. DURING THE PUSH; THE MECH CLRED US TO START THE L ENG ONLY; AS MORE LAST-MIN BAGS WERE EXPECTED. ONCE THE BAGS WERE LOADED AND THE FORWARD CARGO DOOR CLOSED; AS PER PROC; WE HAD TO WAIT 1 MIN BEFORE STARTING THE R ENG. THE MECH CLRED US TO START THE R ENG; AND SAID HE WOULD STAND BY ON THE HEADSET. DUE TO THE PROCEDURAL DELAY AND SINCE PUSHBACK WAS COMPLETE WITH THE PARKING BRAKE SET; I SUGGESTED HE COULD DISCONNECT THE TOWBAR. I OBSERVED THE 'NOSEWHEEL STEERING DISCONNECT' MESSAGE DISAPPEAR; FOLLOWED BY THE MECH'S 'TOWBAR DISCONNECTED; PIN REMOVED' CALL. I CLRED HIM TO DISCONNECT HIS HEADSET. HE SAID 'DISCONNECTING; WATCH FOR MY SALUTE.' EARLIER; I HAD NOTICED THE ACFT AT GATE Y; TO OUR R; PUSHBACK BEFORE US AND NOW I LOOKED AND SAW THAT WE WERE IN THEIR WAY AND POSSIBLY DELAYING THEIR TAXI. THIS; ALONG WITH THE FACT THAT WE HAD TO DELAY R ENG START WHICH WOULD DELAY THEM FURTHER; DISTR ME AND I ASKED THE FO IF HE WAS AGREEABLE TO A SINGLE-ENG TAXI OUT NOW AND STARTING THE R ENG DURING TAXI. HE SAID HE WAS AND WE CONFIGURED ACCORDINGLY. AT THIS POINT; IN MY MIND; I SOMEHOW MISTAKENLY ASSUMED THAT I HAD RECEIVED THE 'SALUTE AND RELEASE FROM GUIDANCE' SIGNAL. IN THE HURRY AND DISTR; I BELIEVE MY MIND COMPUTED THE 'TOWBAR DISCONNECTED PIN REMOVED.' CALL AS THE 'SALUTE AND RELEASE FROM GUIDANCE' SIGNAL. I THEN TURNED THE ANTISKID AND NOSEWHEEL STEERING SWITCH ON; SET MY ACP TO VHF2 AND SAID 'TAXI CLRNC.' WE WERE CLRED TO TAXI BY RAMP CTL. I CALLED 'L CLR' AND THE FO CALLED 'R CLR.' I TURNED ON THE TAXI LIGHT; RELEASED THE PARKING BRAKE AND MOVED FORWARD. JUST THEN THE FO CALLED 'STOP' AND I IMMEDIATELY STOPPED THE ACFT. I ESTIMATE I HAD MOVED 3-4 FT. THE FO THEN SAID HE NOW SAW THE TUG EMERGING INTO HIS FIELD OF VIEW FROM BENEATH THE ACFT. THE MECH CONTINUED MOVING THE TUG FURTHER; PARKED; AND GAVE ME THE 'SALUTE AND RELEASE FROM GUIDANCE' SIGNAL. WE TAXIED OUT WITHOUT FURTHER INCIDENT. THERE WAS NO FELT OR RPTED DAMAGE TO PERSONNEL OR EQUIP. CRITIQUE: IN THE HURRY AND DISTR; I MISTOOK THE 'TOWBAR DISCONNECTED; PIN REMOVED' CALL TO BE THE 'SALUTE AND RELEASE FROM GUIDANCE' SIGNAL AND PROCEEDED FROM THAT MISCONCEPTION. THE FO ALSO DID NOT CATCH MY MISSED 'I HAVE A SALUTE AND RELEASE FROM GUIDANCE' CALL. MY FAILURE TO RECOGNIZE THE RED FLAGS OF BEING HURRIED AND DISTR LED TO THIS BREAKDOWN OF SOP'S.