theorem sbeh {x: nat} (a: nat) (b c: wff x): $ F/ x c $ > $ x = a -> (b <-> c) $ > $ [a / x] b <-> c $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hyp h | F/ x c |
|
2 | 1 | sbeht | A. x (x = a -> (b <-> c)) -> ([a / x] b <-> c) |
3 | hyp e | x = a -> (b <-> c) |
|
4 | 3 | ax_gen | A. x (x = a -> (b <-> c)) |
5 | 2, 4 | ax_mp | [a / x] b <-> c |