theorem eex {x: nat} (a: wff x) (b: wff): $ a -> b $ > $ E. x a -> b $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | con1 | (~b -> A. x ~a) -> ~A. x ~a -> b |
|
| 2 | 1 | conv ex | (~b -> A. x ~a) -> E. x a -> b |
| 3 | con3 | (a -> b) -> ~b -> ~a |
|
| 4 | hyp h | a -> b |
|
| 5 | 3, 4 | ax_mp | ~b -> ~a |
| 6 | 5 | iald | ~b -> A. x ~a |
| 7 | 2, 6 | ax_mp | E. x a -> b |