Theorem bian12da | index | src |

theorem bian12da (G a b c d: wff):
  $ G /\ d -> (a <-> b /\ c) $ >
  $ G -> (d /\ a <-> b /\ (d /\ c)) $;
StepHypRefExpression
1 anlass
d /\ (b /\ c) <-> b /\ (d /\ c)
2 hyp h
G /\ d -> (a <-> b /\ c)
3 2 aneq2da
G -> (d /\ a <-> d /\ (b /\ c))
4 1, 3 syl6bb
G -> (d /\ a <-> b /\ (d /\ c))

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)