theorem
  for L being Element of ProjectiveLines real_projective_plane holds
  ex p,q st p <> q & L = Line(p,q)
  proof
    let L be Element of ProjectiveLines real_projective_plane;
    L in ProjectiveLines real_projective_plane;
    then L in {B where B is Subset of real_projective_plane:
                 B is LINE of real_projective_plane} by INCPROJ:def 1;
    then ex B be Subset of real_projective_plane st L = B &
      B is LINE of real_projective_plane;
    hence thesis by COLLSP:def 7;
  end;
