Theorem imeqi | index | src |

theorem imeqi (a b c d: wff): $ a <-> b $ > $ c <-> d $ > $ a -> c <-> b -> d $;
StepHypRefExpression
1 bitr
(a -> c <-> b -> c) -> (b -> c <-> b -> d) -> (a -> c <-> b -> d)
2 hyp h1
a <-> b
3 2 imeq1i
a -> c <-> b -> c
4 1, 3 ax_mp
(b -> c <-> b -> d) -> (a -> c <-> b -> d)
5 hyp h2
c <-> d
6 5 imeq2i
b -> c <-> b -> d
7 4, 6 ax_mp
a -> c <-> b -> d

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)