Description: Relationship between restricted universal and existential quantifiers. (Contributed by NM, 21-Jan-1997) Allow shortening of rexnal . (Revised by Wolf Lammen, 9-Dec-2019)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | dfral2 | |- ( A. x e. A ph <-> -. E. x e. A -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | notnotb | |- ( ph <-> -. -. ph ) |
|
| 2 | 1 | ralbii | |- ( A. x e. A ph <-> A. x e. A -. -. ph ) |
| 3 | ralnex | |- ( A. x e. A -. -. ph <-> -. E. x e. A -. ph ) |
|
| 4 | 2 3 | bitri | |- ( A. x e. A ph <-> -. E. x e. A -. ph ) |