User:Dfeuer/Class Bounded by Set is Set
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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.
$\blacksquare$