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 |