ACCELERATING AT 10000 SAW SMA TWIN PASS AT ESTIMATED 10200.

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ON CLB OUT; ASSIGNED 13000 FT MSL ON ASSIGNED HDG OF 220 DEG; PASSING 10000 FT MSL; I HAD JUST CALLED FOR THE ALTIMETER CHK REQUIRED BY COMPANY AT 10000 FT. THE FO WAS FLYING; THE CAPT HAD JUST SIGNALED THE FLT ATTENDANTS THAT STERILE COCKPIT HAD TERMINATED (AT 10000 MSL) WHEN HE CAME ON THE CTLS AS HE SPOTTED TFC XING L TO R HDG APPROX 360 DEG; ALT APPROX 10200 FT. CAPT DID NOT ASSUME CTL BUT POINTED OUT TFC TO FO. ESTIMATE MISS DISTANCE AT 200 FT. CAPT CALLED DEP CTL; THEY HAD NO READOUT ON THE AIRPLANE UNTIL JUST AFTER WE WENT UNDER HIM. HIS READOUT THEN WAS RPTED AS 10400 FT MSL. ORD TCA EXTENDS TO 20 MI UP TO 10000 FT MSL. WE WERE AT 17 NM AND CLBING THROUGH 10000 FT. TECHNICALLY; NO ONE IS AT FAULT. LESSONS LEARNED: TFC WATCH MUST BE MAINTAINED WITH VIGILANCE THROUGH FL180. ESPECIALLY IN AN AREA LIKE CHICAGO WITH SO MUCH TFC. AIRPLANE WE WERE IN HAD NOT BEEN UPGRADED WITH THE TCAS SYS. MY OPINION IS THAT TCAS WOULD HAVE BEEN VERY HELPFUL IN THIS SITUATION. SUPPLEMENTAL INFO FROM ACN 184638. THE CAPT QUERIED THE CTLR ABOUT THE LIGHT TWIN. THE CTLR'S RESPONSE WAS; 'OK.' THE CAPT; AGAIN; QUESTIONED THE CTLR. THIS TIME; THE CTLR ACKNOWLEDGED A TARGET THAT; APPARENTLY; JUST POPPED UP 4 MI N OF OUR POS AT 10400 FT.