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 Th11:
  not p1,p2,q1 are_collinear & p1,p2,q2 are_collinear & q1,q2,q3
  are_collinear & q2<>q3 implies not p2,p1,q3 are_collinear
proof
  assume that
A1: not p1,p2,q1 are_collinear and
A2: p1,p2,q2 are_collinear and
A3: q1,q2,q3 are_collinear and
A4: q2<>q3;
A5: p1<>p2 by A1,ANPROJ_2:def 7;
  assume
A6: not thesis;
  then p1,p2,q3 are_collinear by Th1;
  then p1,q2,q3 are_collinear by A2,A5,Th2;
  then
A7: q2,q3,p1 are_collinear by Th1;
  p2,p1,q2 are_collinear by A2,Th1;
  then p2,q2,q3 are_collinear by A6,A5,Th2;
  then
A8: q2,q3,p2 are_collinear by Th1;
  q2,q3,q1 are_collinear by A3,Th1;
  hence contradiction by A1,A4,A7,A8,ANPROJ_2:def 8;
end;
