theorem nfan {x: nat} (a b: wff x): $ F/ x a $ > $ F/ x b $ > $ F/ x a /\ b $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hyp h1 | F/ x a |
|
| 2 | hyp h2 | F/ x b |
|
| 3 | 2 | nfnot | F/ x ~b |
| 4 | 1, 3 | nfim | F/ x a -> ~b |
| 5 | 4 | nfnot | F/ x ~(a -> ~b) |
| 6 | 5 | conv an | F/ x a /\ b |