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

theorem
  ex C being U-petit Category st C is non U-element
  proof
    assume
A1: not ex C being U-petit Category st C is non U-element;
    consider C be U-petit Category such that
    the carrier of C is Element of U and
A2: not the carrier' of C is Element of U by Th64;
    not C is U-element by A2;
    hence thesis by A1;
  end;
