theorem nfsbid (G: wff) {x: nat} (A B: set x): $ G -> A == B $ > $ G -> ((FS/ x A) <-> (FS/ x B)) $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hyp h | G -> A == B |
|
2 | 1 | eleq2d | G -> (y e. A <-> y e. B) |
3 | 2 | nfeqd | G -> ((F/ x y e. A) <-> (F/ x y e. B)) |
4 | 3 | aleqd | G -> (A. y (F/ x y e. A) <-> A. y (F/ x y e. B)) |
5 | 4 | conv nfs | G -> ((FS/ x A) <-> (FS/ x B)) |