Description: Relationship between restricted universal and existential quantifiers. (Contributed by NM, 21-Jan-1997) (Proof shortened by Wolf Lammen, 9-Dec-2019)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | rexnal | |- ( E. x e. A -. ph <-> -. A. x e. A ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dfral2 | |- ( A. x e. A ph <-> -. E. x e. A -. ph ) |
|
| 2 | 1 | con2bii | |- ( E. x e. A -. ph <-> -. A. x e. A ph ) |