Theorem false_imp_true_iff_true ≪ | index | src | ≫

\imp真值表：\false \imp \true \iff \true

theorem false_imp_true_iff_true: $ \false \imp \true \iff \true $;
StepHypRefExpression
1 iff_comp 
((\neg \true \imp \true) \imp \true) \imp (\true \imp \neg \true \imp \true) \imp (\neg \true \imp \true \iff \true)
2 neg_imp_tosame 
(\neg \true \imp \true) \imp \true
3 1, 2 ax_mp 
(\true \imp \neg \true \imp \true) \imp (\neg \true \imp \true \iff \true)
4 introl_imp 
\true \imp \neg \true \imp \true
5 3, 4 ax_mp 
\neg \true \imp \true \iff \true
6 5 conv false 
\false \imp \true \iff \true

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3)