Axiom:Identity of Betweenness

Axiom
Let $\mathsf{B}$ be the relation of betweenness.

Let $=$ be the relation of equality.

Then the following axiom holds:
 * $\forall a,b: \mathsf{B}aba \implies a = b$

where $a$ and $b$ are points.

Intuition
If between a point and itself lies another point, we're dealing with exactly one point.