Where can I find a list of proof identities?

AI Thread Summary
A user seeks a reliable source for a list of proof identities, specifically basic concepts like disjoint and if-then statements in logic symbols. They express a desire to verify their understanding and explore additional identities. The user later shares a helpful resource, ProofWiki, which contains definitions and explanations of various proof identities. The provided links direct to specific categories and definitions relevant to the inquiry. ProofWiki is recommended as a valuable tool for those looking to enhance their knowledge of proof identities.
Stickybees
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Does anyone know if there is a good place to find a list of proof identities? Basic stuff like the disjoint or if-then in logic symbols. It would be nice to have a place to make sure I'm remembering them correctly and to search for more.

Thanks!
 
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Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
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