Definition:Mapping/Class Theory

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Let $V$ be a basic universe.

A mapping $f$ in the context of Class Theory is a relation such that:

$f \subseteq V \times V$:
$\forall x \in \Dom f: \exists! y \in \Img f: \tuple {x, y} \in f$

That is, for every $x$ in the domain of $f$, there exists exactly one $y$ in the image of $f$ such that $\tuple {x, y} \in f$.