"Some bad conduct discharges come with a felony upon discharge, but not all."
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You have absolutely no idea what you're taking about- a service member gets an OTH and in this case a bad conduct discharge BECAUSE they have been convicted of a Court Marshall offense, which would have been tantamount to felony assault- especially if he had instead been dishonorably discharged for domestic abuse.  If the system had that information, the Lautenberg Amendment would have stopped him from buying.  He lied on his background check and omitted his OTH.