Axiom:Density of Betweenness

Axiom
Let $a,b,c,d$ be points.

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

Let $\ne$ be the relation of being distinct.

Then express the density of betweenness by the sentence:


 * $\forall a,b: \exists c: a \ne b \implies c \ne a \land c \ne b \land \mathsf{B}acb$

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