User:Dfeuer/Subclass of Set is Set

Axiom

Let $s$ be a set.

Let $T$ be a class.

Then:

If $T$ is a subclass of $s$, then $T$ is a set.

That is, if $\mathbb U$ is the universal class, then:

$\forall s: \forall T: (s \in \mathbb U \land T \subseteq s \implies T \in \mathbb U)$

That is, $\mathbb U$ is swelled.