Using results

(i)	R4843: Conditional entropy formula for simple mutual information
(ii)	R4837: Chain rule for simple entropy in the binary case

we have \begin{equation} I_a(X ; Y) = H_a(X) - H_a(X \mid Y) = H_a(X) + H_a(Y) - H_a(X, Y) \end{equation} $\square$