Description: Absorption of existence condition by uniqueness. (Contributed by NM, 4-Nov-2002) Shorten proof and avoid df-eu . (Revised by BJ, 14-Oct-2022)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | moabs | |- ( E* x ph <-> ( E. x ph -> E* x ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-1 | |- ( E* x ph -> ( E. x ph -> E* x ph ) ) |
|
| 2 | nexmo | |- ( -. E. x ph -> E* x ph ) |
|
| 3 | id | |- ( E* x ph -> E* x ph ) |
|
| 4 | 2 3 | ja | |- ( ( E. x ph -> E* x ph ) -> E* x ph ) |
| 5 | 1 4 | impbii | |- ( E* x ph <-> ( E. x ph -> E* x ph ) ) |