If A is true, we use the following Hilbert axiom A->(B->A) with A=B and Modus Ponens, then we get A->A?
If I remember correctly, this is a valid argument in Hilbert's axiom system and one of the first proofs that one does. You could take a look at Introduction to Mathematical Logic by Elliott Mendelson to double check, and I also would recommend that you focus on Isabelle related questions, and check if people have asked something similar before.
Last updated: Dec 30 2024 at 16:22 UTC