Metamath Proof Explorer


Theorem exnal

Description: Existential quantification of negation is equivalent to negation of universal quantification. Dual of alnex . See also the dual pair df-ex / alex . Theorem 19.14 of Margaris p. 90. (Contributed by NM, 12-Mar-1993)

Ref Expression
Assertion exnal
|- ( E. x -. ph <-> -. A. x ph )

Proof

Step Hyp Ref Expression
1 alex
 |-  ( A. x ph <-> -. E. x -. ph )
2 1 con2bii
 |-  ( E. x -. ph <-> -. A. x ph )