
theorem Th58:
  for l1,l2,l3 being Element of ProjectiveLines real_projective_plane st
  l1,l2,l3 are_concurrent holds dual l1,dual l2,dual l3 are_collinear
  proof
    let l1,l2,l3 be Element of ProjectiveLines real_projective_plane;
    assume l1,l2,l3 are_concurrent;
    then consider P be Point of real_projective_plane such that
A1: P in l1 & P in l2 & P in l3;
    reconsider lP = dual P as Element of ProjectiveLines real_projective_plane;
    dual l1 in lP & dual l2 in lP & dual l3 in lP by A1,Th54;
    hence thesis by Th57;
  end;
