Open Ball contains Smaller Open Ball

Theorem
Let $M = \struct{A, d}$ be a metric space.

Let $a \in A$.

Let $\epsilon, \delta \in \R_{\gt 0}$ such that $\epsilon \le \delta$.

Let $\map {B_\epsilon} a, \map {B_\delta} a$ be the open balls centered on $a$ of radii $\epsilon$ and $\delta$ respectively.

Then:
 * $\map {B_\epsilon} a \subseteq \map {B_\delta} a$

Proof
By definition of subset:
 * $\map {B_\epsilon} a \subseteq \map {B_\delta} a$