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