Let $M_X = (X, d_X)$ and $M_Y = (Y, d_Y)$ each be a D1107: Metric space.
Let $f : X \to Y$ be a D47: Lipschitz map with respect to $M_X$ and $M_Y$.

Then $f$ is a D3333: Hölder map with respect to $M_X$ and $M_Y$.