
theorem Th60:
  for l1,l2,l3 being Element of ProjectiveLines real_projective_plane holds
  l1,l2,l3 are_concurrent iff dual l1, dual l2, dual l3 are_collinear
  proof
    let l1,l2,l3 be Element of ProjectiveLines real_projective_plane;
    hereby
      assume l1,l2,l3 are_concurrent;
      then dual dual l1,l2,l3 are_concurrent by Th46;
      then dual dual l1,dual dual l2,l3 are_concurrent by Th46;
      then dual dual l1,dual dual l2,dual dual l3 are_concurrent by Th46;
      hence dual l1, dual l2, dual l3 are_collinear by Th59;
    end;
    assume dual l1, dual l2, dual l3 are_collinear;
    then dual dual l1, dual dual l2, dual dual l3 are_concurrent by Th59;
    then l1, dual dual l2, dual dual l3 are_concurrent by Th46;
    then l1, l2, dual dual l3 are_concurrent by Th46;
    hence thesis by Th46;
  end;
