Theorem oreqi | index | src |

theorem oreqi (a b c d: wff): $ a <-> b $ > $ c <-> d $ > $ a \/ c <-> b \/ d $;
StepHypRefExpression
1 bitr
(a \/ c <-> b \/ c) -> (b \/ c <-> b \/ d) -> (a \/ c <-> b \/ d)
2 hyp h1
a <-> b
3 2 oreq1i
a \/ c <-> b \/ c
4 1, 3 ax_mp
(b \/ c <-> b \/ d) -> (a \/ c <-> b \/ d)
5 hyp h2
c <-> d
6 5 oreq2i
b \/ c <-> b \/ d
7 4, 6 ax_mp
a \/ c <-> b \/ d

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)