theorem nfbi {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 | 1, 2 | nfim | F/ x a -> b |
| 4 | 2, 1 | nfim | F/ x b -> a |
| 5 | 3, 4 | nfan | F/ x (a -> b) /\ (b -> a) |
| 6 | 5 | conv iff | F/ x a <-> b |