Union of Intersections of 2 from 3 equals Intersection of Unions of 2 from 3

Theorem

Let $A$, $B$ and $C$ be sets.

Then:

$\paren {A \cap B} \cup \paren {B \cap C} \cup \paren {C \cap A} = \paren {A \cup B} \cap \paren {B \cup C} \cap \paren {C \cup A}$