In other treatments of elementary geometry, using different sets of axioms, Pasch's axiom can be proved as a theorem; it is a consequence of the plane separation axiom when that is taken as one of the axioms.
The statement explains how Pasch's axiom can be established as a theorem in various geometry texts by employing different sets of axioms. It also highlights that this proof relies on the plane separation axiom, which becomes a foundational assumption for its validity.