
theorem Th57:
  for l being Element of ProjectiveLines real_projective_plane
  for P,Q,R being Point of real_projective_plane st
  P in l & Q in l & R in l holds P,Q,R are_collinear
  proof
    let l be Element of ProjectiveLines real_projective_plane;
    let P,Q,R be Point of real_projective_plane;
    assume
A1: P in l & Q in l & R in l;
    l is LINE of real_projective_plane by INCPROJ:1;
    hence thesis by A1,COLLSP:16;
  end;
