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 Th2:
  a<>b & a,b,c are_collinear & a,b,d are_collinear implies a,c,d are_collinear
proof
A1: a,b,a are_collinear by ANPROJ_2:def 7;
  assume a<>b & a,b,c are_collinear & a,b,d are_collinear;
  hence thesis by A1,ANPROJ_2:def 8;
end;
