reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem Th25:
  p<>q implies ex r st not p,q,r are_collinear
proof
  assume p<>q;
  then consider r such that
A1: not p,q // p,r by Th13;
  take r;
  thus thesis by A1;
end;
