Theorem biim2a | index | src |

theorem biim2a (a b: wff): $ (b -> ~a) -> (a -> b <-> ~a) $;
StepHypRefExpression
1 inot
(a -> ~a) -> ~a
2 imim2
(b -> ~a) -> (a -> b) -> a -> ~a
3 2 imp
(b -> ~a) /\ (a -> b) -> a -> ~a
4 1, 3 syl
(b -> ~a) /\ (a -> b) -> ~a
5 4 exp
(b -> ~a) -> (a -> b) -> ~a
6 absurd
~a -> a -> b
7 6 a1i
(b -> ~a) -> ~a -> a -> b
8 5, 7 ibid
(b -> ~a) -> (a -> b <-> ~a)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)