theorem eexh {x: nat} (a b: wff x): $ F/ x b $ > $ 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 | hyp h1 | F/ x b |
|
| 4 | 3 | nfnot | F/ x ~b |
| 5 | con3 | (a -> b) -> ~b -> ~a |
|
| 6 | hyp h2 | a -> b |
|
| 7 | 5, 6 | ax_mp | ~b -> ~a |
| 8 | 4, 7 | ialdh | ~b -> A. x ~a |
| 9 | 2, 8 | ax_mp | E. x a -> b |