I am looking for a proof for a formula seen on Wikipedia:
\begin{align} I(X;Y|Z) & = H(Z|X) + H(X) + H(Z|Y) + H(Y) - H(Z|X,Y) - H(X,Y) - H(Z) \\ {} & = I(X;Y) + H(Z|X) + H(Z|Y) - H(Z|X,Y) - H(Z) \end{align}
I checked the ref given on Wiki but couldn't find the formula in it.
Thank you!