reserve Omega, I for non empty set;
reserve Sigma for SigmaField of Omega;
reserve P for Probability of Sigma;
reserve D, E, F for Subset-Family of Omega;
reserve  B, sB for non empty Subset of Sigma;
reserve b for Element of B;
reserve a for Element of Sigma;
reserve p, q, u, v for Event of Sigma;
reserve n, m for Element of NAT;
reserve S, S9, X, x, y, z, i, j for set;

theorem Th6:
  for A being Subset-Family of Omega st A is intersection_stable &
  A c= Indep(B,P) holds sigma(A) c= Indep(B,P)
proof
  reconsider Indp = Indep(B,P) as Dynkin_System of Omega by Th5;
  let A be Subset-Family of Omega;
  assume A is intersection_stable & A c= Indep(B,P);
  then sigma(A) c= Indp by DYNKIN:24;
  hence thesis;
end;
