Theorem anim2a | index | src |

theorem anim2a (a b c: wff): $ (a -> b -> c) -> a /\ b -> a /\ c $;
StepHypRefExpression
1 anrl
(a -> b -> c) /\ (a /\ b) -> a
2 anrr
(a -> b -> c) /\ (a /\ b) -> b
3 anl
(a -> b -> c) /\ (a /\ b) -> a -> b -> c
4 1, 3 mpd
(a -> b -> c) /\ (a /\ b) -> b -> c
5 2, 4 mpd
(a -> b -> c) /\ (a /\ b) -> c
6 1, 5 iand
(a -> b -> c) /\ (a /\ b) -> a /\ c
7 6 exp
(a -> b -> c) -> a /\ b -> a /\ c

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)