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 x ¬ φ ¬ x φ


Step Hyp Ref Expression
1 alex x φ ¬ x ¬ φ
2 1 con2bii x ¬ φ ¬ x φ