Bow out/end "conversation" with online bully/harasser?

How do you bow out of, or end, a conversation with a stubborn and arrogant person, without giving them the satisfaction of thinking they "won" an argument? [Mind you, this is on social media. And yes, it should've been put to a stop long ago. But here we are, and the question is still valid.]

I'm usually pretty passive. But occasionally there comes a comment/person who I simply cannot tolerate, or stand by and watch them bully another person, or mock them for their beliefs. Even if the bullying is of the, very real, cyber variety.

Last week, I saw, what was a very clear mockery of someone's stance on an issue. And I stood up to them. I called them on it, in as a respectful, but firm, manner as I could.

And wowzers... didn't take too long hefore he showed his true colors: deflecting, projecting, and patronizing like you wouldn't believe. And when I called him on his condescension, he literally said "Darling, I'll patronize you until the cows come home." He then had the nerve to say I was the one not acting the adult.

This is the God's honest truth: I never once spoke down to him, or used any childish language or tactics. (Even though I'd be well within my "right" to.) Only held him to what is his responsibility to prove his point, and expose the tactics he would use. And when he would attack me personally (which was someplace in every comment), I would stand my ground with facts and then redirect back to the issue. (e.g. "You are a little girl, throwing a fit." "No, you are using ad homimens to avoid responsibility." or similar. But many were much more sly in nature.) Sometimes I wouldn't at all, because some were so petty and baiting that they were not worth acknowledging.

I don't cave easily (to bullies and harassers, of which I've had my share) and said so just in the last day or so. But dang, dude has been at it for a week! He's like a cognitive dissonant dog with a bone. I want to just end it. And I'll admit, I'm feeling a bit of stubbornness myself, but only because I don't want potential future readers to see an outright bully "win." I want them to see and know that they don't have to take that crap.

I suppose there is one good thing at the least-- the other person is no longer the target...

What do I do now though? Is there anything that can be done? A list of facts about the "conversation" perhaps? Resorting to using the same kind of language, cursing, and talking down to them is not an option.