User:Dfeuer/Class Bounded by Set is Set

Theorem
Let $A$ be a class which is bounded by a set $m$.

Then $A$ is a set.

Proof
Since $A$ is bounded by $m$, each element of $A$ is a subset of $m$. That is, $A \subseteq \mathcal P(m)$.

By the power set axiom, $\mathcal P(m)$ is a set.

Thus by the subset axiom, $A$ is a set.