Theorem bieq ≪ | index | src | ≫ 

theorem bieq (a b c d: wff):
  $ (a <-> b) -> (c <-> d) -> (a <-> c <-> (b <-> d)) $;
StepHypRefExpression
1 anl 
(a <-> b) /\ (c <-> d) -> (a <-> b)
2 anr 
(a <-> b) /\ (c <-> d) -> (c <-> d)
3 1, 2 bieqd 
(a <-> b) /\ (c <-> d) -> (a <-> c <-> (b <-> d))
4 3 exp 
(a <-> b) -> (c <-> d) -> (a <-> c <-> (b <-> d))

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)