
theorem
  for l,l1,m,m1 being Element of ProjectiveLines
  real_projective_plane holds ex n being Element of ProjectiveLines
  real_projective_plane st l,l1,n are_concurrent &
  m,m1,n are_concurrent
  proof
    let l,l1,m,m1 be Element of ProjectiveLines
      real_projective_plane;
    consider R be Point of real_projective_plane such that
A1: dual l, dual l1, R are_collinear and
A2: dual m, dual m1, R are_collinear by ANPROJ_2:def 14;
    dual dual l, dual dual l1, dual R are_concurrent &
      dual dual m, dual dual m1, dual R are_concurrent by A1,A2,Th59;
    then l, dual dual l1, dual R are_concurrent &
      m, dual dual m1, dual R are_concurrent by Th46;
    then l, l1, dual R are_concurrent &
      m, m1, dual R are_concurrent by Th46;
    hence thesis;
  end;
