theorem nfsbh {x y: nat} (a: nat x y) (b: wff x y):
$ FN/ x a $ >
$ F/ x b $ >
$ F/ x [a / y] b $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | hyp h1 | FN/ x a |
|
| 2 | 1 | nfeq2 | F/ x z = a |
| 3 | nfv | F/ x y = z |
|
| 4 | hyp h2 | F/ x b |
|
| 5 | 3, 4 | nfim | F/ x y = z -> b |
| 6 | 5 | nfal | F/ x A. y (y = z -> b) |
| 7 | 2, 6 | nfim | F/ x z = a -> A. y (y = z -> b) |
| 8 | 7 | nfal | F/ x A. z (z = a -> A. y (y = z -> b)) |
| 9 | 8 | conv sb | F/ x [a / y] b |