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,a)).f = [[Hom(cod f,a),Hom(dom f,a)],hom(
  f, a ) ]
proof
  assume Hom(C) c= V;
  hence (hom-?(V,a)).f = (hom-?(a)).f by Def25
    .= [[Hom(cod f,a),Hom(dom f,a)],hom(f,a)] by Def21;
end;
