Description: Universal quantification of negation is equivalent to negation of existential quantification. Dual of exnal (but does not depend on ax-4 contrary to it). See also the dual pair df-ex / alex . Theorem 19.7 of Margaris p. 89. (Contributed by NM, 12-Mar-1993)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | alnex | |- ( A. x -. ph <-> -. E. x ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-ex | |- ( E. x ph <-> -. A. x -. ph ) |
|
| 2 | 1 | con2bii | |- ( A. x -. ph <-> -. E. x ph ) |