Theorem animd | index | src |

theorem animd (a b c d e: wff):
  $ a -> b -> c $ >
  $ a -> d -> e $ >
  $ a -> b /\ d -> c /\ e $;
StepHypRefExpression
1 anl
b /\ d -> b
2 hyp h1
a -> b -> c
3 1, 2 syl5
a -> b /\ d -> c
4 3 imp
a /\ (b /\ d) -> c
5 anr
b /\ d -> d
6 hyp h2
a -> d -> e
7 5, 6 syl5
a -> b /\ d -> e
8 7 imp
a /\ (b /\ d) -> e
9 4, 8 iand
a /\ (b /\ d) -> c /\ e
10 9 exp
a -> b /\ d -> c /\ e

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)