
theorem Th07:
  for L being LINE of IncProjSp_of real_projective_plane
  for P,Q being Element of ProjectiveSpace TOP-REAL 3 st
  P <> Q & P in L & Q in L holds L = Line(P,Q)
  proof
    let L be LINE of IncProjSp_of real_projective_plane;
    let P,Q be Element of ProjectiveSpace TOP-REAL 3;
    assume that
A1: P <> Q and
A2: P in L and
A3: Q in L;
    reconsider L9 = L as LINE of real_projective_plane by INCPROJ:4;
    L9 = Line(P,Q) by A1,A2,A3,COLLSP:19;
    hence thesis;
  end;
