Theorem pimex12 | index | src |

theorem pimex12 {x: nat} (p q: wff x): $ (P. x p -> q) -> E. x (p /\ q) $;
StepHypRefExpression
1 exim
A. x (p -> p /\ q) -> E. x p -> E. x (p /\ q)
2 ian
p -> q -> p /\ q
3 2 a2i
(p -> q) -> p -> p /\ q
4 3 alimi
A. x (p -> q) -> A. x (p -> p /\ q)
5 1, 4 syl
A. x (p -> q) -> E. x p -> E. x (p /\ q)
6 5 impcom
E. x p /\ A. x (p -> q) -> E. x (p /\ q)
7 6 conv pim
(P. x p -> q) -> E. x (p /\ q)

Axiom use

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