OPERROR LTSS WHEN AN ACR E120 CONFLICTS WITH A COMPANY E120 AT 6000 FT AFTER RECEIVING; READING BACK AND BEGINNING A DSCNT TO 6000 FT.

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WE WERE APCHING SFO FROM THE SE. AS PER NORMAL PRACTICE WE HAD BEEN DSNDED TO 8000 FT PRIOR TO ENTERING BAY'S AIRSPACE. BAY APCH THEN; AGAIN AS PER NORMAL PRACTICE; CLRED US TO DSND AND MAINTAIN 6000 FT. MY FO READ BACK THE 6000 FT CLRNC AND I ACKNOWLEDGED IT BY SETTING 6000 FT IN THE ALT ALERTER AND HOLDING MY FINGER THERE UNTIL HE ACKNOWLEDGED ME. DSNDING THROUGH 7000 FT I NOTICED A TARGET ON OUR TCASI (BFG TCAS-91). I SELECTED THE CLOSEST RANGE (5 NM) TO BETTER VISUALIZE THE TARGET. THE TARGET (ACFT B) WAS AT OUR 10-11 O'CLOCK POS; 1-2 MI; AND 1000 FT BELOW US; AND WE APPEARED TO BE SLOWLY OVERTAKING THEM. IN OTHER WORDS THEY WERE WHERE WE WERE SUPPOSED TO GO. I QUICKLY ACQUIRED THE TARGET VISUALLY (THEY WERE POPPING IN AND OUT OF THE CLOUD TOPS). SINCE THIS ACFT APPEARED TO BE AT 6000 FT AND WE WERE CLRED TO 6000 FT; WHICH BOTH MY FO AND I RECONFIRMED WITH EACH OTHER AND WITH THE ALT ALERTER; I SLOWED MY DSCNT AND WE ASKED ATC IF THEY HAD ANY TFC THERE. THE CTLR RESPONDED CASUALLY THAT HE DID; IT WAS A COMPANY EMB120 AT 6000 FT GOING IN THE SAME DIRECTION. HIS DEMEANOR IMPLIED; WHY ARE YOU ASKING?; HE IS NO FACTOR. AT THIS TIME WE WERE DSNDING THROUGH 6700-6600 FT. I RESPONDED THAT WE HAD THE ACFT (ACFT B) IN SIGHT; WE HAD BEEN CLRED TO 6000 FT; DID THEY WANT US TO GO BACK UP TO 7000 FT? BAY APCH DID WANT US TO CLB BACK TO 7000 FT; AND WE STOPPED OUR DSCNT BY 6500 FT.