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 Th18:
  for D being Dynkin_System of Omega for x,y being Element of D
  holds x c= y implies y\x in D
proof
  let D be Dynkin_System of Omega;
  let x,y be Element of D;
A1: (x \/ y`)` = x` /\ y`` by XBOOLE_1:53
    .= y\x by SUBSET_1:13;
  assume x c= y;
  then x c= y``;
  then
A2: x misses y` by SUBSET_1:23;
  y`in D by Def5;
  then x \/ y` in D by A2,Th17;
  hence thesis by A1,Def5;
end;
