Is the Convex hull of a simple polygon, and the convex hull of the vertices on a Euclidian plane (that make up the simple polygon), the same set?

Question

This seems pretty intuitive and obvious but I am unable to find explicit evidence. Consider a simple polygon (no holes, no intersecting edges) on a plane. Its convex hull is set A. Consider just the vertices that make up a simple polygon. Is the convex hull of the vertices a subset of A?

In other words, is the convex hull of a planar set, also the convex hull of any simple polygon formed by the same vertices?

It seems obvious but my searches have not yielded an answer.