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\neg \forall x \neg F(x)   

in English could we write this

as Not for all x F(x) holds

or as Not for all x F(x) holds is false.

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$\neg \forall x \neg F(x)$  

$\text{Not for all x F(x) holds is false.}$

$\text{English translation is equivalent to saying for this formula : }$  $\exists F(x) $

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