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

theorem Th88:
  for C being Category holds (C is U-element iff CatToSet C is U-set)
  proof
    let C be Category;
    now
      hereby
        assume C is U-element;
        then the carrier of C is Element of U &
        the carrier' of C is Element of U &
        the Source of C is Element of U &
        the Target of C is Element of U &
        the Comp of C is Element of U by Th54;
        hence CatToSet C is Element of U by Th13;
        hence CatToSet C is U-set;
      end;
    end;
    hence thesis by Th14;
  end;
