LTSS OCCURRED BTWN A BA41 AND DC9 WHEN CTLR MISSED INCORRECT ALT READBACK BY THE FLC OF BA41. OPERROR.

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I WAS THE PF. WE CHKED IN WITH DEP CTL. THEY IMMEDIATELY ASSIGNED US AN ALT OF 4000 FT MSL. UPON REACHING 4000 FT MSL; ATC ASSIGNED US 6000 FT MSL. THE CAPT AND I BOTH HEARD AND UNDERSTOOD A CLB TO 6000 FT MSL. THE CAPT CLRLY READ BACK 'CLB TO 6000 FT MSL' AND DIALED 6000 FT MSL INTO THE ALT SELECTOR. REACHING 5000 FT MSL; ATC ADVISED US THAT A DC9 WOULD BE XING OVER OUR ALT 1000 FT ABOVE US. WHAT THAT MEANT TO ME IS THAT SINCE WE WERE CLRED TO; AND CLBING TO; 6000 FT MSL. HE MUST BE AT 7000 FT MSL. AT ABOUT THAT TIME THE TCASII SYS GAVE US A TA WARNING AND ATC ASKED US IF WE HAD THE TFC IN SIGHT AT 3-4 O'CLOCK ABOVE US; A DC9. I LOOKED OUT THE WINDOW AND SAW THE TFC AND THE CAPT ACKNOWLEDGED TO ATC; 'TFC IN SIGHT.' CLBING THROUGH ABOUT 5100 FT MSL; THE TCASII GAVE US AN RA WARNING; WARNING US 'DON'T CLB.' THE CAPT THEN TOLD ME; 'AS LONG AS YOU HAVE THE TFC IN SIGHT; WE CAN DISREGARD THE RA AND CONTINUE OUR CLB.' RELUCTANTLY; I DID; AND CONTINUED TO CLB TO ABOUT 5500 FT MSL. WHEN SUDDENLY; WITH THE TCASII TELLING US TO 'DON'T CLB AND MONITOR VERT SPD' AND THE DC9 CLOSING IN ON US. I SENSED SOMETHING WASN'T RIGHT AND I LEVELED OFF AT 5500 FT MSL. THE DC9 THEN ASKED ATC 'WHAT WAS OUR ALT?' ATC THEN TOLD US TO 'MAINTAIN 5000 FT MSL.' MY CAPT REPLIED TO ATC; 'WE ARE DSNDING BACK DOWN TO 5000 FT MSL.' THE DC9 PASSED OVER US AND NO FURTHER CONFLICT AROSE. WHEN ON THE GND; THE CAPT AND I CALLED STL DEP CTL AND SPOKE WITH THE SUPVR ON DUTY. HE TOLD US; AFTER LISTENING TO THE ATC TAPES; WE WERE ONLY CLRED TO 5000 FT MSL; HOWEVER; THAT WE CLRLY READ BACK 6000 FT MSL. THE PROB IS THAT ATC DID FAIL TO CATCH AND CORRECT AN IMPROPER ALT READBACK. PROB #2; ATC SHOULD HAVE ADVISED US OF EXACTLY THE ALT THE DC9 WAS AT; IE; TFC AT 6000 FT MSL; INSTEAD OF JUST SAY ALT 1000 FT ABOVE YOU. THE LESSON LEARNED HERE: WHENEVER IN DOUBT AND SOMETHING DOESN'T FEEL RIGHT; TRUST YOUR TCASII -- IT DOESN'T MAKE HUMAN ERRORS!