theorem pimex12 {x: nat} (p q: wff x): $ (P. x p -> q) -> E. x (p /\ q) $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 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) |