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,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;
