I'm sure the fundamental theorem of arithmetic has a non-obvious proof. And perhaps that's precisely what a mathematician means every time they say "non-obvious". If that were all just made explicit to this general interest site in the first place, perhaps we'd have nothing to discuss.
But if we are trying to play coy here, 1+1=2 also requires a non-obvious proof to anyone not versed in formal methods. I looked a proof up:
I don't know how long it would take me, working alone, to come up with that proof. It's non-obvious because it took humans probably 100,000 years to come up with it, even though we've had the IQ to do it for a long time. I don't think we could agree on what constitutes a proof of it without some social aspect and convention, so non-obvious by means of proof.
But, we've been using and making predictions about the world using 1+1=2 for very much longer. That seems like a pretty worthwhile definition of obvious.