Let f: D-R satisfy the Lipschitz condition: there exists an L such that for all x,y$\displaystyle \in$D |f(x)-f(y)|<=L|x-y|

Prove that f is uniformly continuous on D

Here is what I have, is this correct?

Let $\displaystyle \epsilon$>0. Choose $\displaystyle \delta$=$\displaystyle \epsilon$/L. Then by the definition of uniform continuity, if |x-y|<$\displaystyle \delta$=$\displaystyle \epsilon$/L, then |f(x)-f(y)|<L$\displaystyle \epsilon$/L=$\displaystyle \epsilon$.