A quantifier, denoted

\begin{align*} \exists! x \>\> P(x), \\ \exists_{= 1} x \>\> P(x), \end{align*}

and read

“there exists exactly one \(x\) such that \(P(x)\)”

which is equivalent to

\begin{equation*} \forall x \exists y : P(x) \iff x = y \end{equation*}

where \(P\) is the quantified predicate.

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• Synonyms