Metamath Proof Explorer

Theorem alnex

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 x ¬ φ ¬ x φ


Step Hyp Ref Expression
1 df-ex x φ ¬ x ¬ φ
2 1 con2bii x ¬ φ ¬ x φ