Theorem aneq1a ≪ | index | src | ≫

theorem aneq1a (a b c: wff): $ (c -> (a <-> b)) -> (a /\ c <-> b /\ c) $;

Step	Hyp	Ref	Expression
1		ancomb	a /\ c <-> c /\ a
2		ancomb	c /\ b <-> b /\ c
3		aneq2a	(c -> (a <-> b)) -> (c /\ a <-> c /\ b)
4	2, 3	syl6bb	(c -> (a <-> b)) -> (c /\ a <-> b /\ c)
5	1, 4	syl5bb	(c -> (a <-> b)) -> (a /\ c <-> b /\ c)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)