Theorem bian22i | index | src |

theorem bian22i (a b c d: wff): $ a <-> b /\ c $ > $ d /\ a <-> d /\ b /\ c $;
StepHypRefExpression
1 bitr4
(d /\ a <-> d /\ (b /\ c)) -> (d /\ b /\ c <-> d /\ (b /\ c)) -> (d /\ a <-> d /\ b /\ c)
2 hyp h
a <-> b /\ c
3 2 aneq2i
d /\ a <-> d /\ (b /\ c)
4 1, 3 ax_mp
(d /\ b /\ c <-> d /\ (b /\ c)) -> (d /\ a <-> d /\ b /\ c)
5 anass
d /\ b /\ c <-> d /\ (b /\ c)
6 4, 5 ax_mp
d /\ a <-> d /\ b /\ c

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)