Unit-Speed Admissible Curve is Critical Point of Riemannian Length iff Geodesic

Theorem
Let $\struct {M, g}$ be a Riemannian manifold.

Let $\gamma$ be a unit-speed admissible curve.

Let $L_g$ the Riemannian length of some admissible curve.

Then $\gamma$ is the critical point of $L_g$ $\gamma$ is geodesic.