Class Intersection Distributes over Class Union

Theorem
Let $A$, $B$ and $C$ be classes.

Then:
 * $A \cap \paren {B \cup C} = \paren {A \cap B} \cup \paren {A \cap C}$

where:
 * $A \cap B$ denotes class intersection
 * $B \cup C$ denotes class union.

Also see

 * Intersection Distributes over Union


 * Class Union Distributes over Class Intersection