
theorem
  for P,Q being Point of real_projective_plane holds
  (P <> Q iff dual P <> dual Q)
  proof
    let P,Q be Point of real_projective_plane;
    now
      assume
A1:   P <> Q;
      assume dual P = dual Q;
      then P = dual dual Q by Th45;
      hence contradiction by A1,Th45;
    end;
    hence thesis;
  end;
