Definition:Transitive Class

Definition
Let $A$ denote a class, which can be either a set or a proper class.

Then $A$ is transitive if it contains every member as a subset.

That is:


 * $ Tr A \iff \forall x \in A: x \subseteq A$

Since $x \in A \iff x \subseteq \bigcup A$, this can also be expressed as:
 * $\bigcup A \subseteq A$