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 Th13:
  D is Dynkin_System of Omega & D is intersection_stable implies (
  A in D & B in D implies A \/ B in D)
proof
  assume that
A1: D is Dynkin_System of Omega and
A2: D is intersection_stable;
  assume A in D & B in D;
  then A`in D & B`in D by A1,Def5;
  then A`/\ B`in D by A2,FINSUB_1:def 2;
  then (A \/ B)`in D by XBOOLE_1:53;
  then (A \/ B)``in D by A1,Def5;
  hence thesis;
end;
