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

theorem
  for U,V being Universe st U in V holds Ens U is V-small Category
  proof
    let U,V be Universe;
    assume
A1: U in V;
    the carrier of Ens U is U-Class & the carrier' of Ens U is U-Class
      by Th109;
    then Ens U is V-element by A1,CLASSES4:13;
    hence thesis;
  end;
