let P, Q be Point of BK-model-Plane; ( between P,P,Q & between P,Q,Q )
reconsider P2 = BK_to_T2 P, Q2 = BK_to_T2 Q as Point of TarskiEuclid2Space ;
between P2,P2,Q2
by GTARSKI1:17;
hence
between P,P,Q
by Th05; between P,Q,Q
between P2,Q2,Q2
by GTARSKI1:14;
hence
between P,Q,Q
by Th05; verum