reserve FCPS for up-3-dimensional CollProjectiveSpace;
reserve a,a9,b,b9,c,c9,d,d9,o,p,q,r,s,t,u,x,y,z for Element of FCPS;

theorem
  not a,b,c are_collinear & a,b,b9 are_collinear & a<>b9 implies not a,b9,
  c are_collinear
proof
  assume that
A1: not a,b,c are_collinear and
A2: a,b,b9 are_collinear and
A3: a<>b9;
  assume
A4: not thesis;
  a,b9,b are_collinear by A2,Th1;
  hence contradiction by A1,A3,A4,COLLSP:6;
end;
