Let $(X,d_X)$ and $(Z,d_Z)$ be metric spaces, let $Y\subset X$ carry the subspace metric $d_Y:Y\times Y\to [0,\infty)$ defined by $d_Y(y_1,y_2)=d_X(y_1,y_2)$ for all $y_1,y_2\in Y$, and let $f:X\to Z$ be Lipschitz with constant $L\geq 0$. Then the restriction $f|_Y:Y\to Z$ is Lipschitz with constant $L$.