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

theorem
  for X being set st union X is Set of U holds X is Set of U
  proof
    let X be set;
    assume union X is Set of U;
    then union X is U-set by Def10;
    then X is U-set by Th21;
    hence thesis by Def10;
  end;
