Definition:Existential Quantifier/Unique

Definition
The symbol $\exists !$ denotes the existence of a unique object fulfilling a particular condition.


 * $\exists ! x: \map P x$

means:
 * There exists exactly one object $x$ such that $\map P x$ holds

or:
 * There exists one and only one $x$ such that $\map P x$ holds.

Definition 3
The symbol $\exists !$ is a variant of the existential quantifier $\exists$: there exists at least one.

Also see

 * Equivalence of Definitions of Unique Existential Quantifier