Proof of Levy's metric, triangle inequality.

Let http://www.sosmath.com/CBB/latexrend...57b132cbda.png be the set of all functions http://www.sosmath.com/CBB/latexrend...2805fd0649.png which are the distribution functions of some random variables. Proove that function

http://www.sosmath.com/CBB/latexrend...8d6331290c.png

is a metric on the set http://www.sosmath.com/CBB/latexrend...57b132cbda.png (Levy's metric).

I have problem with proving triangle inequality. Does anyone know how can I do that?