Description: Inference adding restricted universal quantifier to both sides of an equivalence. (Contributed by NM, 23-Nov-1994) (Revised by Mario Carneiro, 17-Oct-2016) (Proof shortened by Wolf Lammen, 4-Dec-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | ralbii.1 | |- ( ph <-> ps ) |
|
| Assertion | ralbii | |- ( A. x e. A ph <-> A. x e. A ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ralbii.1 | |- ( ph <-> ps ) |
|
| 2 | 1 | imbi2i | |- ( ( x e. A -> ph ) <-> ( x e. A -> ps ) ) |
| 3 | 2 | ralbii2 | |- ( A. x e. A ph <-> A. x e. A ps ) |