Description: Inference adding restricted existential 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, 6-Dec-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | rexbii.1 | |- ( ph <-> ps ) |
|
| Assertion | rexbii | |- ( E. x e. A ph <-> E. x e. A ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | rexbii.1 | |- ( ph <-> ps ) |
|
| 2 | 1 | a1i | |- ( x e. A -> ( ph <-> ps ) ) |
| 3 | 2 | rexbiia | |- ( E. x e. A ph <-> E. x e. A ps ) |