How to prove $\operatorname{val}(f) = f^+(X)-f^-(X)$ in flow networks?

Question

In flow networks, for any subset $X$, the $\operatorname{val}(f) = f^+(X) - f^-(X)$. What is this theorem called and how can I prove it?

I know that $f^-(\mathrm{sink}) - f^+(\mathrm{sink})=\sum\limits_{v \in X} f^+(v)-\sum\limits_{v \in X} f^-(v) $. But then I don't know how to simplify it...

$val(f) = f^-(\mathrm{sink}) - f^+(\mathrm{sink})$

Thanks