[infinityetc]

What helped me to learn proofs was applying the logic and axioms they relied on over and over again. When working through problem sets (or doing extra problems for study), don't just stop when you can cite the theorem, but work through why it's applicable to that specific use case.

You can then start working through the general cases, until that's the way that you start viewing the problems in the first place. If you decide to go further in math, this process will really prove out (pun intended), as the basic logic will stick with you, even if you don't remember the name of the theorem you're trying to use.