The thing with science is that's pretty universal.
Let's say that the US suddenly discovers the cure to cancer - they're going to publish that in a paper ASAP so that they look better.
Then, the UK will look at that paper - because it's the cure to cancer, of course. The UK will then use this paper to teach others about the cure to cancer - and the cycle goes on and on. So it doesn't matter who you take it from, you should get very similar material.
As for calculations/proofs - if Zumdahl is what it sounds like it is, you'll either find more or less calculations depending on what you think chemistry is. As for proofs, lower levels of chemistry have no proofs - it's an experimental field, you can't really "prove" anything without having experiments to back it up. (note: physical chemistry will have proofs of equations, but of the few I've seen, they were probably more akin to "derivations" than "proofs" - the practical sciences use maths as a language, they aren't maths.

You also shouldn't see any of these equations until first year uni chem anyway, and probably won't be expected to follow the derivations.)