Let (X,d) be a metric space and let D:X*X-->R be defined by:

D(x,y) = (0 if x=y), (max(1,d(x,y)) otherwise)

Prove that (X,D) is a metric space.

I know that I have to show (X,D) is positive definite, symmetric and satisfies the triangle inequality.

The first I am comfortable with. However, I am not sure of how to go about showing symmetry for the x/=y case...same for the triangle inequality. Anybody have any hints or suggestions?