Dynkin System Closed under Intersections is Sigma-Algebra

Theorem
Let $X$ be a set, and let $\mathcal D$ be a Dynkin system on $X$.

Suppose that $\mathcal D$ satisfies the following condition:


 * $(1):\quad \forall D, E \in \mathcal D: D \cap E \in \mathcal D$

That is, $\mathcal D$ is closed under intersection.

Then $\mathcal D$ is a $\sigma$-algebra.