Definition:Bounded Class/Bounded Subset of Class

Definition
Let $B$ be a class. Let $B$ be a subclass of a class $A$.

Then $B$ is a bounded subset of $A$ :
 * there exists a set $x \in A$ such that $B$ is bounded by $x$

That is, every element of $B$ is a subset of $x$.

Also see

 * Definition:Set Bounded by Set