'RHOA' Matt Jordan Says Fight Video Proves His Claim, Peter Thomas Pulled a Knife

Matt Jordan insists the only reason he didn't kick Peter Thomas' ass quicker is because Peter had a knife on him, and now that we've finally seen the video ... Matt might have a point.

Matt, ex-bf of 'RHOA' star Kenya Moore, tells us Peter pulled the knife out when he went at him. He claims Peter tried to hide it so it would seem like he was beating Matt fair and square.

When we called Peter, he admitted he had a box cutter on him because he owns a restaurant and night club. He says he only pulled it out in self-defense -- "If I was an idiot I would have sliced him, but I'm not. I wasn't there to fight with Matt."

When we slo-mo'd the video, you can clearly see the blade in Peter's hand during the struggle.

Matt, who'd previously made the knife claim, says he was focused on wrestling it away at first, but once he turned his attention to Peter ... he took him down easily. He adds, "Peter knows what it is."

Peter is pressing assault charges, but also feels he got the best of Matt ... as he bragged to us in March, right after the fight went down.