An image was posted to a website or websites, with the certification number blacked out, which invalidates the "certificate," regardless of whether this image is otherwise authentic or not.
So, no, he hasn't given proof of his eligibility.
Excuses, excuses. Conspiracy theorists love to “debunk” this or that. The problem is, they never give any reason why anyone should believe them. They don’t have to. They “love” the Constitution. That should be enough for everyone else to abandon reason and logic.