Description: Universal quantifier in terms of existential quantifier and negation. Dual of df-ex . See also the dual pair alnex / exnal . Theorem 19.6 of Margaris p. 89. (Contributed by NM, 12-Mar-1993)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | alex | |- ( A. x ph <-> -. E. x -. ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | notnotb | |- ( ph <-> -. -. ph ) |
|
| 2 | 1 | albii | |- ( A. x ph <-> A. x -. -. ph ) |
| 3 | alnex | |- ( A. x -. -. ph <-> -. E. x -. ph ) |
|
| 4 | 2 3 | bitri | |- ( A. x ph <-> -. E. x -. ph ) |