TFC SEPARATION IS LOST BTWN DEP AND ARR ACR'S NEAR CLT; NC.

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CLRNC WAS VIA 'UNARM ARR' TO CLT. ZTL ISSUED CLRNC TO CROSS ADENA AT 12000 FT; NORMAL SPD. AT ADENA; WE CONTACTED CLT APCH AND HE SAID TO EXPECT RWY 18R APCH. WE WERE THEN ISSUED A CLRNC TO 7000 FT. BOTH THE FO AND I HEARD 7000 FT. I READ BACK 7000 FT AND WE BOTH VERIFIED 7000 FT WAS SET IN FMA. ACFT WAS SLOWED TO 250 KTS AND WE DSNDED. AT APPROX 8500 FT; APCH SAID TO STOP DSCNT AND CLB BACK TO 9000 FT. AT APPROX 8300 FT; A CLB BACK TO 9000 FT WAS INITIATED. THE TCASII ISSUED A TFC ALERT; BUT NO TFC AVOIDANCE COMMANDS WERE ISSUED BY TCASII. THE REASON WAS A B737 ON DEP VECTOR WAS PROCEEDING FROM R TO L AT 12 O'CLOCK POS AT 7000 FT AT APPROX 3 MI. WE TOLD THE APCH CTLR WE WERE SURE A CLRNC HAD BEEN ISSUED TO 7000 FT AND ASKED IF HE WANTED A CALL ON THE GND; BUT HE SAID NO AND WE CONTINUED WITH A NORMAL APCH AND LNDG. I HAVE NO SUGGESTIONS AS TO HOW TO AVOID THIS TYPE OF PROB. I BELIEVE WE WERE MISTAKENLY CLRED TO 7000 FT. HOWEVER; THE SYS WORKED AS IT SHOULD HAVE. IF THE CTLR HAD NOT ISSUED A CLB; I AM SURE THE TCASII WOULD HAVE.