reserve Omega, F for non empty set,
  f for SetSequence of Omega,
  X,A,B for Subset of Omega,
  D for non empty Subset-Family of Omega,
  n,m for Element of NAT,
  h,x,y,z,u,v,Y,I for set;

theorem Th22:
  for E being Subset-Family of Omega st E is intersection_stable
  holds generated_Dynkin_System(E) is intersection_stable
proof
  let E be Subset-Family of Omega such that
A1: E is intersection_stable;
  reconsider G=generated_Dynkin_System(E) as Subset-Family of Omega;
  for a,b being set st a in G & b in G holds a/\ b in G by A1,Th21;
  hence thesis by FINSUB_1:def 2;
end;
