Theorem bitr4gi | index | src |

theorem bitr4gi (a b c d: wff):
  $ c <-> a $ >
  $ d <-> b $ >
  $ a <-> b $ >
  $ c <-> d $;
StepHypRefExpression
1 bitr
(c <-> a) -> (a <-> d) -> (c <-> d)
2 hyp h1
c <-> a
3 1, 2 ax_mp
(a <-> d) -> (c <-> d)
4 bitr4
(a <-> b) -> (d <-> b) -> (a <-> d)
5 hyp h
a <-> b
6 4, 5 ax_mp
(d <-> b) -> (a <-> d)
7 hyp h2
d <-> b
8 6, 7 ax_mp
a <-> d
9 3, 8 ax_mp
c <-> d

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)