reserve V for non empty set,
  A,B,A9,B9 for Element of V;
reserve f,f9 for Element of Funcs(V);
reserve m,m1,m2,m3,m9 for Element of Maps V;
reserve a,b for Object of Ens(V);
reserve f,g,f1,f2 for Morphism of Ens(V);
reserve C for Category,
  a,b,a9,b9,c for Object of C,
  f,g,h,f9,g9 for Morphism of C;

theorem
  Hom(C) c= V implies hom??(V,C).[f opp,g] = [[Hom(cod f,dom g),Hom(dom
  f,cod g)],hom(f,g)]
proof
  assume
A1: Hom(C) c= V;
  thus (hom??(V,C)).[f opp,g] = (hom??(C)).[f,g] by A1,Def26
    .= [[Hom(cod f,dom g),Hom(dom f,cod g)],hom(f,g)] by Def23;
end;
