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

theorem Th96:
  for C being U-small Category holds C is U-locally_small
  proof
    let C be U-small Category;
    now
      let x,y be Object of C;
      Hom(x,y) c= the carrier' of C &
        the carrier' of C is Element of U by Def17;
      hence Hom(x,y) is U-set by CLASSES4:13;
    end;
    hence thesis;
  end;
