Theorem bian21i | index | src |

theorem bian21i (a b c d: wff): $ a <-> b /\ c $ > $ a /\ d <-> b /\ d /\ c $;
StepHypRefExpression
1 bitr
(a /\ d <-> b /\ c /\ d) -> (b /\ c /\ d <-> b /\ d /\ c) -> (a /\ d <-> b /\ d /\ c)
2 hyp h
a <-> b /\ c
3 2 aneq1i
a /\ d <-> b /\ c /\ d
4 1, 3 ax_mp
(b /\ c /\ d <-> b /\ d /\ c) -> (a /\ d <-> b /\ d /\ c)
5 anrass
b /\ c /\ d <-> b /\ d /\ c
6 4, 5 ax_mp
a /\ d <-> b /\ d /\ c

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)