Composition of Mappings is Associative

Theorem
The composition of mappings is an associative binary operation:

$$\left({f_3 \circ f_2}\right) \circ f_1 = f_3 \circ \left({f_2 \circ f_1}\right)$$

Proof
Follows directly from:
 * A mapping is a relation;
 * The composition of relations is associative.