Power Set of Transitive Set is Transitive

Theorem
Let $x$ be a transitive set.

Then its power set $\powerset x$ is also a transitive set.

Proof
Let $x$ be transitive.

By Set is Transitive iff Subset of Power Set:
 * $x \subseteq \powerset x$

Then by Power Set of Subset:
 * $\powerset x \subseteq \powerset {\powerset x}$

Thus by Set is Transitive iff Subset of Power Set:
 * $\powerset x$ is a transitive set.