theorem exim {x: nat} (a b: wff x): $ A. x (a -> b) -> E. x a -> E. x b $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 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 |