Looking for references for learning the words and sentences used in proofs

Question

I'm familiar with textbooks on logic, proof techniques, and sets. But I have yet to encounter a textbook that dives into the language used w/ definitions and sentence structure used in proofs, for example(when to use the word "claim" in a proof and its meaning and what you have to deduce by saying that, or what does it mean to use the word "fix" on an element and its meaning. Or when should you use "without loss of generality" and its meaning, you get the picture. In other words, proof writing