Axiom:Density of Betweenness

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

Let $=$ be the relation of equality.

Then the density of betweenness is expressed by the statement:
 * $\forall a,b: \exists c: \neg \left({a = b}\right) \implies \neg \left({c = a}\right)\land \neg \left({c = b}\right) \land \mathsf{B}acb$

where $a,b,c$ are points.

Intuition
Between any two distinct points you can draw a third point, distinct from both.