Let $M$ be a smooth manifold equipped with a Riemannian distance $d$, let $f:M\to M$ be a $C^1$ diffeomorphism, and let $\Lambda\subset M$ be a compact hyperbolic $f$-invariant set. Then $f|_\Lambda:\Lambda\to\Lambda$ is expansive: there exists $c>0$ such that, if $x,y\in\Lambda$ satisfy