Theorem iman | index | src |

theorem iman (a b: wff): $ a -> b <-> ~(a /\ ~b) $;
StepHypRefExpression
1 bitr4
(a -> b <-> a -> ~~b) -> (~(a /\ ~b) <-> a -> ~~b) -> (a -> b <-> ~(a /\ ~b))
2 notnot
b <-> ~~b
3 2 imeq2i
a -> b <-> a -> ~~b
4 1, 3 ax_mp
(~(a /\ ~b) <-> a -> ~~b) -> (a -> b <-> ~(a /\ ~b))
5 notan2
~(a /\ ~b) <-> a -> ~~b
6 4, 5 ax_mp
a -> b <-> ~(a /\ ~b)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)