theorem biim2a (a b: wff): $ (b -> ~a) -> (a -> b <-> ~a) $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inot | (a -> ~a) -> ~a |
|
2 | imim2 | (b -> ~a) -> (a -> b) -> a -> ~a |
|
3 | 2 | imp | (b -> ~a) /\ (a -> b) -> a -> ~a |
4 | 1, 3 | syl | (b -> ~a) /\ (a -> b) -> ~a |
5 | 4 | exp | (b -> ~a) -> (a -> b) -> ~a |
6 | absurd | ~a -> a -> b |
|
7 | 6 | a1i | (b -> ~a) -> ~a -> a -> b |
8 | 5, 7 | ibid | (b -> ~a) -> (a -> b <-> ~a) |