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

theorem Th109:
  Ens U is non U-small Category & the carrier of (Ens U) is U-Class &
  the carrier' of (Ens U) is U-Class
  proof
A1: not the carrier of (Ens U) in U;
    then not Ens U is U-element;
    hence (Ens U) is non U-small Category;
    the carrier of (Ens U) c= U;
    hence the carrier of (Ens U) is U-Class by A1;
    thus thesis by Th108;
  end;
