$I(X,Y,Z)$ and $I(X\bigcup Y,Z,W) \ge I(X,Y,W)$

Question

I am trying to prove if $I(X,Y,Z)$ and $I(X\bigcup Y,Z,W)=> I(X,Y,W)$. I know that $I(X,Y|Z)=I(Y,X|Z)$ and $I(X,W|Z\bigcup Y)$ and $I(X,Y|Z) \Rightarrow I(X,Y\bigcup W|Z)$, unable to use the above the axioms, to the question. Can anyone explain what needs to be done here?