Description: Introduce unique existential quantifier to both sides of an equivalence. (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 6-Oct-2016)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | eubii.1 | |- ( ph <-> ps ) |
|
| Assertion | eubii | |- ( E! x ph <-> E! x ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eubii.1 | |- ( ph <-> ps ) |
|
| 2 | eubi | |- ( A. x ( ph <-> ps ) -> ( E! x ph <-> E! x ps ) ) |
|
| 3 | 2 1 | mpg | |- ( E! x ph <-> E! x ps ) |