So I am looking to show:
$$I(X;Y|Z) = I(Y;Z|X) − I(Y;Z) + I(X;Y)$$
I started with rewriting it with the sum
$$\sum_{x,y,z} p_{XYZ}\log_2\frac{p_{XY}(x,y|z)}{p_X(x|z)p_Y(y|z)}$$
But I do not really know where to go from there.
Do i need to split it up?
Cheers, Avocari