ATX X CLB TO OCCUPIED ALT HAD LTSS FROM ACR Y. SYS ERROR.

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ATX X DEPARTED DETROIT CITY ARPT; CLBING SBOUND TO FL130; REQUESTING FL160. ACR Y; OVERFLT NWBOUND AT FL160. UPON ENTERING MY AIRSPACE; I CLBED X TO FL160. WENT AND DID A COUPLE OTHER CTLR ACTIONS. I REALIZED MY MISTAKE. I TRIED TO STOP ATX X AT FL150. PLT READ BACK THAT HE WAS DSNDING BACK DOWN TO FL150. HAD X GET Y IN SIGHT AND MAINTAIN VISUAL SEPARATION. SUPPLEMENTAL INFO FROM ACN 303338: ON A FLT FROM DETROIT CITY ARPT TO MANSFIELD OHIO; THE FOLLOWING OCCURRED. WE WERE FLYING A LEARJET ON VECTORS MAINTAINING A HDG OF 210 DEGS S OF DETROIT. WE WERE CLBING ON A CLRNC TO 16000 FT. CLBING THROUGH 15500 FT; THE CTLR ASKED US TO DSND TO 15000 FT ADDING THERE WAS TFC AT 1 O'CLOCK AND 1 MI AT 16000 FT ON A PERPENDICULAR HDG. WE IDENTED THE TFC VISUALLY. I IMMEDIATELY INITIATED A DSCNT STOPPING THE CLB AT 15600 FT. THE TFC PASSED OVERHEAD AS WE WERE DSNDING THROUGH 15500 FT; THEREFORE PASSING 500 FT ABOVE US. THE REST OF THE FLT CONTINUED WITHOUT INCIDENT. SUPPLEMENTAL INFO FROM ACN 302350: ATC THEN CALLED 'TFC 8-9 O'CLOCK LEVEL 16000 FT;' WE BOTH LOOKED. I COULD NOT SEE THE TFC BECAUSE OF ITS RELATIVE POS; ABOVE AND DIRECTLY OFF THE L WING. THE CAPT COULD SEE IT AND ADVISED ATC 'TFC IN SIGHT.' WE WERE TOLD TO MAINTAIN VISUAL SEPARATION WITH THE TFC; WHICH THE PF DID. DSNDING BACK THROUGH 15700 FT A BEECH 1900 PASSED DIRECTLY OVERHEAD; WHICH WAS THE FIRST I HAD SEEN THE TFC.