Value of Relation is Small

Theorem
The value of a relation is always a small class.

Proof
Let $\mathcal R$ be an arbitrary relation.

Let $s$ be any set.

The value of a relation is either equal to some set $y$ or $\varnothing$ by Uniqueness Condition for Relation Value.

If it is equal to some set $y$, then the value of $s$ under $\mathcal R$ is a small class by the definition of small class.

If it is equal to $\varnothing$, then the result follows from Empty Set is Small.