Description: Equality theorem for restricted class abstractions. (Contributed by NM, 15-Oct-2003) Avoid ax-10 , ax-11 , ax-12 . (Revised by Gino Giotto, 20-Aug-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | rabeq | |- ( A = B -> { x e. A | ph } = { x e. B | ph } ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eleq2 | |- ( A = B -> ( x e. A <-> x e. B ) ) |
|
| 2 | 1 | anbi1d | |- ( A = B -> ( ( x e. A /\ ph ) <-> ( x e. B /\ ph ) ) ) |
| 3 | 2 | rabbidva2 | |- ( A = B -> { x e. A | ph } = { x e. B | ph } ) |