I was reading Wilde's 'Quantum Information Theory' and saw the following theorem at chapter 11 $(11.7.2)$:

$$
I(A; B | C) \ge 0, ........ (1)
$$
where,
$$
I(A;B|C) := H(A|C) + H(B | C) - H(AB|C). 
$$

I know that the mutual information is non-negative, i.e. 
$$
I(A;B) \ge 0,
$$
where,
$$
I(A;B) := H(A) + H(B) - H(AB).
$$
Now if we have access to an additional subsystem $C$, this can't decrease the mutual information of $A$ and $B$. But I was looking for sort of formal proof of this. I was trying to apply the non-negativity of mutual info. into this, but not sure how to proceed. Thanks in advance!