Let (X,dx) and (Y,dy) be two metric spaces and f: X-->Y be a mapping satisfying the Lipshitz condition

dy(f(x),f(y))<(or equal to) Ldx(x,y), L does not equal zero, for all x,y elements of X.

is this uniform continuous and if so how would does anyone know what proof would be used well to prove it?

i'll check it this site very frequently so any help will be appreciated. thnx.