# Axiom:Transitivity of Equidistance

## Axiom

Let $\equiv$ be the relation of equidistance.

Then the following axiom holds:

$\forall a,b,p,q,r,s: \left({ab \equiv pq \land ab \equiv rs}\right) \implies pq \equiv rs$

where $a, b, p, q, r, s$ are points.

## Intuition

If a line segment has the same length as two others, those two others have the same length as each other.