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
  not p1,p2,q1 are_collinear & p1,p2,p3 are_collinear & q1,q2,p3
  are_collinear & p3<>q2 & p2<>p3 implies not p3,p2,q2 are_collinear
proof
  assume that
A1: not p1,p2,q1 are_collinear and
A2: p1,p2,p3 are_collinear and
A3: q1,q2,p3 are_collinear and
A4: p3<>q2 and
A5: p2<>p3;
  assume
A6: not thesis;
  p3,p2,p1 are_collinear by A2,Th1;
  then
A7: p3,q2,p1 are_collinear by A5,A6,Th2;
A8: p3,q2,q1 are_collinear by A3,Th1;
  p3,q2,p2 are_collinear by A6,Th1;
  hence contradiction by A1,A4,A7,A8,ANPROJ_2:def 8;
end;
