Theorem and_comm | index | src |

\and交换

theorem and_comm (A B: wff): $ A \and B \iff B \and A $;
StepHypRefExpression
1 iff_intro_neg
(A \imp \neg B \iff B \imp \neg A) \imp (\neg (A \imp \neg B) \iff \neg (B \imp \neg A))
2 imp_neg_perm
A \imp \neg B \iff B \imp \neg A
3 1, 2 ax_mp
\neg (A \imp \neg B) \iff \neg (B \imp \neg A)
4 3 conv and
A \and B \iff B \and A

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3)