theorem imeqi (a b c d: wff): $ a <-> b $ > $ c <-> d $ > $ a -> c <-> b -> d $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bitr | (a -> c <-> b -> c) -> (b -> c <-> b -> d) -> (a -> c <-> b -> d) |
|
2 | hyp h1 | a <-> b |
|
3 | 2 | imeq1i | a -> c <-> b -> c |
4 | 1, 3 | ax_mp | (b -> c <-> b -> d) -> (a -> c <-> b -> d) |
5 | hyp h2 | c <-> d |
|
6 | 5 | imeq2i | b -> c <-> b -> d |
7 | 4, 6 | ax_mp | a -> c <-> b -> d |