\begin{definition}[Definition:Existential Quantifier/Unique]
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'''.
This quantifier is called the '''unique existential quantifier'''.
\end{definition}