Intersection is Associative

Theorem
Set intersection is associative:


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

Proof
Therefore:
 * $x \in A \cap \paren {B \cap C}$ $x \in \paren {A \cap B} \cap C$

Thus it has been shown that:
 * $A \cap \paren {B \cap C}\ = \paren {A \cap B} \cap C$

Also see

 * Union is Associative
 * Set Difference is not Associative
 * Symmetric Difference is Associative