theorem bitrd (a b c d: wff): $ a -> (b <-> c) $ > $ a -> (c <-> d) $ > $ a -> (b <-> d) $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hyp h1 | a -> (b <-> c) |
|
2 | 1 | bi1d | a -> b -> c |
3 | hyp h2 | a -> (c <-> d) |
|
4 | 3 | bi1d | a -> c -> d |
5 | 2, 4 | syld | a -> b -> d |
6 | 3 | bi2d | a -> d -> c |
7 | 1 | bi2d | a -> c -> b |
8 | 6, 7 | syld | a -> d -> b |
9 | 5, 8 | ibid | a -> (b <-> d) |