
theorem
  for P being Element of BK_model
  for L being LINE of IncProjSp_of real_projective_plane
  holds ex Q being Element of ProjectiveSpace TOP-REAL 3 st P <> Q & Q in L
  proof
    let P be Element of BK_model;
    let L be LINE of IncProjSp_of real_projective_plane;
    consider p,q be Point of real_projective_plane such that
A2: p <> q and
A3: L = Line(p,q) by BKMODEL1:73;
    P <> p or P <> q by A2;
    hence thesis by A3,COLLSP:10;
  end;
