Range of Small Relation is Small

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Theorem

Let $a$ be a small class.

Let $a$ also be a relation.


Then the range of $a$ is small.


Proof

Let $A$ equal:

$\left\{{\left({\left({x, y}\right), y}\right): \left({x, y}\right) \in a}\right\}$

Then, $A$ maps $a$ to its range.

Thus, the range of $a$ is the image of $A$.


By Image of Small Class under Mapping is Small, the range of $a$ is small.


$\blacksquare$


Sources