Theorem bitr3 ≪ | index | src | ≫ 

theorem bitr3 (a b c: wff): $ (b <-> a) -> (b <-> c) -> (a <-> c) $;
StepHypRefExpression
1 anl 
(b <-> a) /\ (b <-> c) -> (b <-> a)
2 anr 
(b <-> a) /\ (b <-> c) -> (b <-> c)
3 1, 2 bitr3d 
(b <-> a) /\ (b <-> c) -> (a <-> c)
4 3 exp 
(b <-> a) -> (b <-> c) -> (a <-> c)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)