theorem sbseh {x: nat} (a: nat) (A B: set x): $ FS/ x B $ > $ x = a -> A == B $ > $ S[a / x] A == B $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hyp h | FS/ x B |
|
2 | 1 | sbseht | A. x (x = a -> A == B) -> S[a / x] A == B |
3 | hyp e | x = a -> A == B |
|
4 | 3 | ax_gen | A. x (x = a -> A == B) |
5 | 2, 4 | ax_mp | S[a / x] A == B |