theorem sbseq2d {x: nat} (G: wff) (a: nat x) (A B: set x): $ G -> A == B $ > $ G -> S[a / x] A == S[a / x] B $;
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hyp h | G -> A == B |
|
2 | 1 | eleq2d | G -> (y e. A <-> y e. B) |
3 | 2 | sbeq2d | G -> ([a / x] y e. A <-> [a / x] y e. B) |
4 | 3 | abeqd | G -> {y | [a / x] y e. A} == {y | [a / x] y e. B} |
5 | 4 | conv sbs | G -> S[a / x] A == S[a / x] B |