theorem notan2 (a b: wff): $ ~(a /\ b) <-> a -> ~b $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom | (a -> ~b <-> ~(a /\ b)) -> (~(a /\ b) <-> a -> ~b) |
|
2 | notnot | a -> ~b <-> ~~(a -> ~b) |
|
3 | 2 | conv an | a -> ~b <-> ~(a /\ b) |
4 | 1, 3 | ax_mp | ~(a /\ b) <-> a -> ~b |