The intersection of $3$ set is empty, would the intersection of $4$ sets be empty? Let me clarify some more.
Let's say we have four sets $A,B,C,$ and $D$.
If the intersection of any three sets is empty, by default is the intersection of all four sets empty?

$A \cap B \cap C \cap D \subseteq A \cap B \cap C = \emptyset$. Thus $A \cap B \cap C \cap D = \emptyset$. 
