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:


 * $(1): \quad \forall a, b, c, p, q: \exists x: \mathsf B a p c \land \mathsf B b q c \implies \mathsf B p x b \land \mathsf B q x a$

and:


 * $(2): \quad \forall a, b, c, p, q: \exists x: \mathsf B a p c \land \mathsf B q c b \implies \mathsf B a x q \land \mathsf B b p x$

are logically equivalent.