reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem Th22:
  X \/ (X /\ Y) = X
proof
  thus X \/ (X /\ Y) c= X
  proof
    let x be object;
    assume x in X \/ (X /\ Y);
    then x in X or x in X /\ Y by XBOOLE_0:def 3;
    hence thesis by XBOOLE_0:def 4;
  end;
  let x be object;
  thus thesis by XBOOLE_0:def 3;
end;
