Description: Equality theorem for restricted universal quantifier. (Contributed by NM, 16-Nov-1995) Remove usage of ax-10 , ax-11 , and ax-12 . (Revised by Steven Nguyen, 30-Apr-2023)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | raleq | |- ( A = B -> ( A. x e. A ph <-> A. x e. B ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | biidd | |- ( A = B -> ( ph <-> ph ) ) |
|
| 2 | 1 | raleqbi1dv | |- ( A = B -> ( A. x e. A ph <-> A. x e. B ph ) ) |