reserve PCPP for CollProjectiveSpace,
  a,a9,a1,a2,a3,b,b9,b1,b2,c,c1,c3,d,d9,e,
  o,p,p1,p2,p3,r,q, q1,q2,q3,x,y for Element of PCPP;

theorem
  ex q,r st not p,q,r are_collinear
proof
  consider q such that
A1: p<>q and
  p<>q and
  p,p,q are_collinear by ANPROJ_2:def 10;
  ex r st not p,q,r are_collinear by A1,Th4;
  hence thesis;
end;
