Hopf-Rinow Theorem/Corollary 1

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

Let $T_p M$ be the tangent space at $p \in M$.

Let $\exp_p$ be the restricted exponential map.

Suppose there is $p \in M$ such that $\exp_p$ is defined on all of $T_p M$.

Then $M$ is complete.