The negation of an existential quantifier is a logical operation that expresses that a certain property does not hold for any member of a specified domain. In symbolic terms, if we have an existential statement like 'There exists an x such that P(x)' represented as $$\exists x P(x)$$, its negation would be 'For all x, P(x) is not true', which is symbolically written as $$\neg(\exists x P(x)) \equiv \forall x \neg P(x)$$. This concept is fundamental in formal logic and helps to understand how statements about existence can be transformed into statements about universal non-existence.
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