
theorem
  for l,m,n,n1,n2 being Element of ProjectiveLines real_projective_plane st
  l <> m & l,m,n are_concurrent & l,m,n1 are_concurrent &
  l,m,n2 are_concurrent holds n,n1,n2 are_concurrent
  proof
    let l,m,n,n1,n2 be Element of ProjectiveLines real_projective_plane;
    assume that
A1: l <> m and
A2: l,m,n are_concurrent and
A3: l,m,n1 are_concurrent and
A4: l,m,n2 are_concurrent;
    dual l <> dual m & dual l,dual m, dual n are_collinear &
      dual l,dual m, dual n1 are_collinear &
      dual l,dual m, dual n2 are_collinear by A1,A2,A3,A4,Th60,Th48;
    then dual dual n, dual dual n1, dual dual n2 are_concurrent
      by ANPROJ_2:def 8,Th59;
    then n, dual dual n1, dual dual n2 are_concurrent by Th46;
    then n, n1, dual dual n2 are_concurrent by Th46;
    hence thesis by Th46;
  end;
