Geometry - Vertical Angles

I recently finished watching the video, Vertical Angles within the section, https://www.khanacademy.org/math/geometry/hs-geo-foundations

The issue is that near the end of the video the author still states that the general statement of vertical angles always being equal hasn't been proven yet.  He states that he will show a proof in the next video.  However the next section is equation practice with vertical angles which automatically assumes that vertical angles are equal.  No proof was ever shown.  What am I missing?