A B757 FLC DEPARTS AFTER AN ACFT CHANGE WITH THE RELEASE STILL INDICATING THE OLD ACFT NUMBER AT PHX; AZ.

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FLT WAS FROM PHX TO MDW. TKOF TIME WAS XY15 AM; PHX LCL. WHEN THE CREW ARRIVED AT THE DEP GATE; THE AGENT SAID WE HAD AN ACFT CHANGE. SO WE ALL WENT TO THE GATE NEXT DOOR TO THE PLANE THAT WE WERE ORIGINALLY SUPPOSED TO TAKE. THE FUELERS WERE FUELING; CATERING WAS ONBOARD DOING THEIR JOB. EVERYTHING WAS AS IT WAS SUPPOSED TO BE. I TOLD THE FO THAT WE NEEDED TO GET A NEW RELEASE BEFORE WE LEFT BECAUSE THE ONE WE HAD WAS THE OLD ACFT. THE LEAD FLT ATTENDANT CAME TO THE COCKPIT WITH A MAINT PROB IN THE BACK SO I WENT BACK WITH MAINT TO FIX THE PROB. MEANWHILE IT WAS 5 MINS PRIOR TO DEP WITH ABOUT 50 PEOPLE AT THE GATE CHKING IN WITH BAGS. SO I WENT BACK TO HELP THE AGENTS. WE FINALLY DEPARTED 10 MINS LATE FROM THE GATE. UPON ARR AT MDW I REALIZED THAT I FORGOT TO GET THE NEW RELEASE. NOW IT WAS TOO LATE. WE LEFT PHX WITH A RELEASE WITH THE WRONG ACFT NUMBER ON IT. IN THE MIDDLE OF THE NIGHT THE CREW IS TIRED BEFORE WE GET TO THE ACFT. NEXT TIME I WILL DELEGATE THE FO TO GET THE RELEASE CHANGED AND I WILL NOT WORRY SO MUCH WITH THE PAX BOARDING. LET THE AGENTS DO THEIR JOB.