Have you done proof based maths before? I restarted my maths education from scratch awhile ago when realising my basic math foundations was shaky. I used basic mathmatics by Serge Lang which makes you prove things as you go. This got me used to proof by induction, and proof by contradiction for simple problems.

That might be bit basic though. Something like the book "how to prove it" or "book of proof" may help get you started.