Theorem exnal

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.)

Conclusion
\( \vdash \exists x \, \neg \varphi \leftrightarrow \neg \forall x \, \varphi \)
Proof
alex
con2bii _