Negation of Uniqueness Quantifier Is there a negation of uniqueness quantifier? I need to negate an expression which includes a uniqueness quantifier.

Just expand the quantifier:

$$ \exists ! x ~ P(x) \equiv \exists x ~ (P(x) \wedge (\forall y ~ P(y) \rightarrow y = x)) $$

and apply the usual negation rules for quantifiers.