theorem sbed (G: wff) {x: nat} (a: nat) (b: wff x) (c: wff):
$ G /\ x = a -> (b <-> c) $ >
$ G -> ([a / x] b <-> c) $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbet | A. x (x = a -> (b <-> c)) -> ([a / x] b <-> c) |
|
| 2 | hyp e | G /\ x = a -> (b <-> c) |
|
| 3 | 2 | ialda | G -> A. x (x = a -> (b <-> c)) |
| 4 | 1, 3 | syl | G -> ([a / x] b <-> c) |