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

theorem
  for c being set st c in card U holds card (bool c) in U
  proof
    let c be set;
    assume c in card U;
    then reconsider c as Element of U by CLASSES2:13;
    card bool c in U by CLASSES4:29;
    hence thesis;
  end;
