A natural deduction proof of $\neg (A \wedge B) \rightarrow (A \rightarrow \neg B)$ without RAA

99 Views Asked by Bumbble Comm At 29 Mar 2026 - 11:27

I am doing (for fun) the exercices of this lean tutorial.

For the third exercice of section 3.6. Exercises:

"Give a natural deduction proof of $\neg (A \wedge B) \rightarrow (A \rightarrow \neg B)$."

I did the following answer:

Since I used a RAA (Reductio ad absurdum - proof by contradiction) rule, I wanted to know if it was possible doing it without this rule.

Edit

Thanks to the comment below of drhab, I realized that I didn't use indeed RAA ; instead it is