The reason I'm only a little surprised is that it's the kind of question I would expect to be in the literature somewhere, either as stated or stated similarly, and I suspect this is why GPT5 can do it.
I am impressed because I know how hard it can be to find an existing proof, having spent a very long time on a problem before finding the solution in a 1950 textbook by Feller. I would not expect this to be at all easy to find.
I can see this ability advancing science in many areas. The number of published papers on medical science is insane. I look forward to medical researchers questions being answered by GPT5 too, although in that case it'd need to provide a citation since proof can be harder to come by.
Also, it's a difficult proof step and if I'd come up with it, I'd be /very/ pleased with myself. Although I suspect GPT5 probably didn't come up with this based on my limited experience using it to try and solve unrelated problems.