Boolean Expression Simplification (De Morgan's) I need to prove that:
$$
!(!(X.W) + !(X.Z))) = X.W.Z
$$
I have tried multiple approaches but cannot figure this out. 
Using DeMorgan's theorem, I break the negative sign binding $XW$, and $XZ$, and change their sign:
$$
!((!X + !W + !X + !Z))
$$
By Indempotent Law, I can keep only one $!X$:
$$
!(!X + !W + !Z) 
$$
What are the next steps?
Edit, adding angryavian's solution: 
Using DeMorgan's Theorem again I can negate !X,!Y,!Z as a group instead of individually, and change their sign (. instead of +): 
$$
!(!(X.W.Z))
$$
Double not (!) negates each other, leaving with the solution: 
$$
X.W.Z
$$

CW answer (from comments to push it from unanswered queue:
Hint: Use DeMorgan's law again
