Union of Transitive Class is Transitive/Proof 1

Proof
Let $A$ be transitive.

By Class is Transitive iff Union is Subclass:
 * $\bigcup A \subseteq A$

By Union of Subclass is Subclass of Union of Class:
 * $\map \bigcup {\bigcup A} \subseteq \bigcup A$

Then by Class is Transitive iff Union is Subclass:
 * $\bigcup A$ is transitive.