Powerset is not Subset of its Set/Proof 2

Theorem

Let $A$ be a set.

Then:

$\powerset A \not \subseteq A$

Proof

Aiming for a contradiction, suppose that $\powerset A \subseteq A$.

Let $I: \powerset A \to A$ be the identity mapping.

$I$ is an injection by Identity Mapping is Injection.

But by No Injection from Power Set to Set, this is a contradiction.

$\blacksquare$