Show that the convex hull of a set S is the intersection of all convex sets that contain S

Question

Show that the convex hull of a set $S$ is the intersection of all convex sets that contain $S$. Suppose $H$ is the convex hull of $S$, and $D$ is the intersection of all convex sets contain $S$. Certainly, it's easy to prove that $H \subset D$, but how to prove that $D \subset H$?