No nuclear-armed country wants to be involved in a nuclear war with another nuclear-armed country. That would be the worst imaginable outcome. Therefore, none of them will use nukes against each other. They may use them against a small country that can't fire back a nuke, and who isn't protected under some security alliance with a large country that has nukes, but that is it. In general, having nukes protects nuclear-capable countries from being attacked by non-nuclear capable countries, and it strongly discourages nuclear-capable countries from fighting each other, but I don't think it stops it. The US and Russia, for instance, may get into a direct war with each other and still nukes won't be used. It is as if they didn't exist, they are of no use against an enemy who also has them. Anything you launch gets launched back at you, so it's is kind of like punching yourself in the balls - something nobody does.

That being said, accidents happen.

I'm about to watch the video now.