reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem Th45:
  for X being set st union X is empty holds X is U-set
  proof
    let X be set;
    assume union X is empty;
    then per cases by ZFMISC_1:33,1,82;
    suppose X = {};
      hence thesis by CLASSES2:56;
    end;
    suppose X = {{}};
      hence thesis by CLASSES2:56,57;
    end;
  end;
