Equivalence of Formulations of Pasch's Axiom

Theorem
The two forms of Pasch's Axiom in Tarski's Geometry are consistent.

That is, the expressions:


 * $(1) \quad \forall a,b,c,p,q \ \exists x :\mathsf{B}apc \land \mathsf{B}bqc \implies \mathsf{B}pxb \land \mathsf{B}qxa$

and:


 * $(2) \quad \forall a,b,c,p,q \ \exists x : \mathsf{B}apc \land \mathsf{B}qcb \implies \mathsf{B}axq \land \mathsf{B}bpx$

are logically equivalent.