Theorem exim | index | src |

theorem exim {x: nat} (a b: wff x): $ A. x (a -> b) -> E. x a -> E. x b $;
StepHypRefExpression
1 con3
(A. x ~b -> A. x ~a) -> ~A. x ~a -> ~A. x ~b
2 1 conv ex
(A. x ~b -> A. x ~a) -> E. x a -> E. x b
3 con3
(a -> b) -> ~b -> ~a
4 3 al2imi
A. x (a -> b) -> A. x ~b -> A. x ~a
5 2, 4 syl
A. x (a -> b) -> E. x a -> E. x b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4)