theorem bibin1 (a b: wff): $ ~a -> (a <-> b <-> ~b) $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | noteq | (a <-> b) -> (~a <-> ~b) |
|
| 2 | 1 | bi1d | (a <-> b) -> ~a -> ~b |
| 3 | 2 | com12 | ~a -> (a <-> b) -> ~b |
| 4 | binth | ~a -> ~b -> (a <-> b) |
|
| 5 | 3, 4 | ibid | ~a -> (a <-> b <-> ~b) |