Axiom:Inner Transitivity of Betweenness

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

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

This axiom asserts that:


 * $\forall a,b,c,d: \mathsf{B}abd \land \mathsf{B}bcd \implies \mathsf{B}abc$

Intuition


Let $abd$ and $bcd$ be line segments.

Suppose they are arranged to form one straight line segment.

Then the points $a,b,c$ are collinear.