Vector Augend plus Addend equals Augend implies Addend is Zero

Theorem
Let $V$ be a vector space over a field $F$.

Let $\mathbf a, \mathbf b \in V$.

Let $\mathbf a + \mathbf b = \mathbf a$.

Then:
 * $\mathbf b = \bszero$

where $\bszero$ is the zero vector of $V$.