let S be satisfying_Tarski-model TarskiGeometryStruct ; for a, b, c, d, p being POINT of S st between4 a,b,c,d & between c,p,d holds
between5 a,b,c,p,d
let a, b, c, d, p be POINT of S; ( between4 a,b,c,d & between c,p,d implies between5 a,b,c,p,d )
assume A1:
( between4 a,b,c,d & between c,p,d )
; between5 a,b,c,p,d
then
( between a,p,d & between a,c,p & between b,c,p & between b,p,d & between c,p,d )
by Satz3p5p1, Satz3p5p2;
hence
between5 a,b,c,p,d
by A1, Satz3p5p1; verum