Hrbacek and Jech is very good, and covers a lot of stuff. But if you only want the basics, a book on proofs may be sufficient, for example "Book of proof" by Richard Hammack or "How to prove it" by Velleman. (I know that the former is good, and there's a free online version if you want to check it out. I'm not familiar with the latter, but it seems to be very popular).