
theorem
  for P being Point of real_projective_plane
  for l being Element of ProjectiveLines real_projective_plane st
  dual l in dual P holds P in l
  proof
    let P be Point of real_projective_plane;
    let l be Element of ProjectiveLines real_projective_plane;
    assume dual l in dual P;
    then dual dual P in dual dual l by Th54;
    then P in dual dual l by Th45;
    hence thesis by Th46;
  end;
