Superset of Dependent Set is Dependent

Theorem
Let $M = \struct {S, \mathscr I}$ be a matroid.

Let $A, B \subseteq S$ such that $A \subseteq B$

If $A$ is a dependent subset then $B$ is a dependent subset.

Proof
From the contrapositive statement of matroid axiom $(\text I 2)$:
 * $A \notin \mathscr I \implies B \notin \mathscr I$

By the definition of a dependent subset:
 * If $A$ is not an dependent subset then $B$ is not an dependent subset.