theorem impim (b: wff) {x: nat} (a c: wff x):
$ (P. x a -> b -> c) -> b -> (P. x a -> c) $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpcom | b -> (b -> c) -> c |
|
| 2 | 1 | imim2d | b -> (a -> b -> c) -> a -> c |
| 3 | 2 | alimd | b -> A. x (a -> b -> c) -> A. x (a -> c) |
| 4 | 3 | anim2d | b -> E. x a /\ A. x (a -> b -> c) -> E. x a /\ A. x (a -> c) |
| 5 | 4 | conv pim | b -> (P. x a -> b -> c) -> (P. x a -> c) |
| 6 | 5 | com12 | (P. x a -> b -> c) -> b -> (P. x a -> c) |