theorem nfsb1h {x: nat} (a: nat x) (b: wff x): $ FN/ x a $ > $ F/ x [a / x] b $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hyp h | FN/ x a |
|
| 2 | 1 | nfeq2 | F/ x z = a |
| 3 | nfal1 | F/ x A. x (x = z -> b) |
|
| 4 | 2, 3 | nfim | F/ x z = a -> A. x (x = z -> b) |
| 5 | 4 | nfal | F/ x A. z (z = a -> A. x (x = z -> b)) |
| 6 | 5 | conv sb | F/ x [a / x] b |