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

theorem
  for C being U-locally_small Category holds C opp is U-locally_small Category
  proof
    let C be U-locally_small Category;
    now
      let x,y be Object of (C opp);
      reconsider oy = opp y, ox = opp x as Object of C;
      Hom(x,y) = Hom(oy,ox) by OPPCAT_1:6;
      hence Hom(x,y) is U-set by Def36;
    end;
    hence thesis by Def36;
  end;
