Umm, that last claim is wholly untrue. Every nuclear-armed country (save perhaps a couple) has detonated nuclear bombs. The US isn't even the only one to use it intentionally against civilians, since the French were actively studying the deleterious effects of fallout on their colonial subjects in French Polynesia, which is what led to the Rainbow Warrior state-sponsored terrorist attack against New Zealand. I'm sure that there are other cases of the USSR or some other nuclear power testing their own devices against civilian populations if I had a mind to check.

Perhaps "the US is the only country to detonate a nuclear weapon against civilians of a country with which it was at war" or "the only country to detonate a nuclear weapon as an act of war"