Theorem neg_elimintror_imp | index | src |

\neg消除右引入\imp

theorem neg_elimintror_imp (A B: wff): $ \neg A \imp A \imp B $;
StepHypRefExpression
1 imp_imp_insl
(\neg A \imp (\neg B \imp \neg A) \imp A \imp B) \imp (\neg A \imp \neg B \imp \neg A) \imp \neg A \imp A \imp B
2 introl_imp
((\neg B \imp \neg A) \imp A \imp B) \imp \neg A \imp (\neg B \imp \neg A) \imp A \imp B
3 neg_imp_elimrev
(\neg B \imp \neg A) \imp A \imp B
4 2, 3 ax_mp
\neg A \imp (\neg B \imp \neg A) \imp A \imp B
5 1, 4 ax_mp
(\neg A \imp \neg B \imp \neg A) \imp \neg A \imp A \imp B
6 introl_imp
\neg A \imp \neg B \imp \neg A
7 5, 6 ax_mp
\neg A \imp A \imp B

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3)