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 Th7:
  not a,b,c are_collinear & a,b,d are_collinear & a,c,d are_collinear
implies a=d
proof
  assume that
A1: not a,b,c are_collinear and
A2: a,b,d are_collinear & a,c,d are_collinear;
  assume
A3: not thesis;
A4: a,d,a are_collinear by ANPROJ_2:def 7;
  a,d,b are_collinear & a,d,c are_collinear by A2,Th1;
  hence contradiction by A1,A3,A4,ANPROJ_2:def 8;
end;
