Theorem biim1a | index | src |

theorem biim1a (a b: wff): $ (~a -> b) -> (a -> b <-> b) $;
StepHypRefExpression
1 anr
(~a -> b) /\ (a -> b) -> a -> b
2 anl
(~a -> b) /\ (a -> b) -> ~a -> b
3 1, 2 casesd
(~a -> b) /\ (a -> b) -> b
4 3 exp
(~a -> b) -> (a -> b) -> b
5 ax_1
b -> a -> b
6 5 a1i
(~a -> b) -> b -> a -> b
7 4, 6 ibid
(~a -> b) -> (a -> b <-> b)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)