There are several rules of inference which utilize the existential quantifier.
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When it appears in a formula together with a predicate variable, they are referred to as an existential quantifier.
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It asserts that a predicate within the scope of an existential quantifier is true of at least one value of a predicate variable.
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An existential formula is a formula starting with a sequence of existential quantification followed by a quantifier-free formula.
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In language as opposed to formal logic, existence is a predicate rather than a quantifier, and the passage from copulative to existential usage can be subtle.