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 Th53:
  hom(id a,id b) = id Hom(a,b)
proof
  thus hom(id a,id b) = hom(a,id b) by Th52
    .= id Hom(a,b) by Th42;
end;
