Theorem bitrd | index | src |

theorem bitrd (a b c d: wff):
  $ a -> (b <-> c) $ >
  $ a -> (c <-> d) $ >
  $ a -> (b <-> d) $;
StepHypRefExpression
1 hyp h1
a -> (b <-> c)
2 1 bi1d
a -> b -> c
3 hyp h2
a -> (c <-> d)
4 3 bi1d
a -> c -> d
5 2, 4 syld
a -> b -> d
6 3 bi2d
a -> d -> c
7 1 bi2d
a -> c -> b
8 6, 7 syld
a -> d -> b
9 5, 8 ibid
a -> (b <-> d)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)