let P, Q be POINT of BK-model-Plane; GTARSKI1:def 10 ( not between P,Q,P or P = Q )
assume A1:
between P,Q,P
; P = Q
reconsider P2 = BK_to_T2 P, Q2 = BK_to_T2 Q as POINT of TarskiEuclid2Space ;
between P2,Q2,P2
by A1, Th05;
hence
P = Q
by GTARSKI1:def 10, Th65; verum