Axiom:Outer Connectivity 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.

This axiom asserts that:


 * $\forall a,b,c,d: \left({\mathsf{B}abc \land \mathsf{B}abd \land a \ne b }\right) \implies \left({\mathsf{B}acd \lor \mathsf{B}adc}\right)$

Also see

 * Inner Connectivity of Betweenness