Theorem imp_boole_def | index | src |

\imp布尔等价式

theorem imp_boole_def (A B: wff): $ A \imp B \iff \neg A \or B $;
StepHypRefExpression
1 iff_intror_imp
(A \iff \neg \neg A) \imp (A \imp B \iff \neg \neg A \imp B)
2 negneg_alloc
A \iff \neg \neg A
3 1, 2 ax_mp
A \imp B \iff \neg \neg A \imp B
4 3 conv or
A \imp B \iff \neg A \or B

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3)