Theorem bitr3g ≪ | index | src | ≫

theorem bitr3g (a b c d e: wff):
  $ b <-> d $ >
  $ c <-> e $ >
  $ a -> (b <-> c) $ >
  $ a -> (d <-> e) $;

Step	Hyp	Ref	Expression
1		bicom	(b <-> d) -> (d <-> b)
2		hyp h1	b <-> d
3	1, 2	ax_mp	d <-> b
4		hyp h2	c <-> e
5		hyp h	a -> (b <-> c)
6	4, 5	syl6bb	a -> (b <-> e)
7	3, 6	syl5bb	a -> (d <-> e)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)