Subset is Element of Power Set

Theorem
Let $x$ be a set.

Let $\powerset x$ denote the power set of $x$.

Then:
 * $y \in \powerset x \iff y \subseteq x$

Proof
By definition of power set, $\powerset x$ is the set of subsets of $x$.

Hence the result, by definition of subset and power set.