Value of Relation is Small
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The value of a relation is always a small class.
Let $\RR$ be an arbitrary relation.
Let $s$ be any set.
The value of a relation is either equal to some set $y$ or $\O$ by Uniqueness Condition for Relation Value.
If it is equal to some set $y$, then the value of $s$ under $\RR$ is a small class by the definition of small class.
If it is equal to $\O$, then the result follows from Empty Set is Small.
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 6.13$