reserve A,B,C for Category,
  F,F1 for Functor of A,B;
reserve o,m for set;
reserve t for natural_transformation of F,F1;

theorem Th12:
  for a1,a2 being Object of A, b1,b2 being Object of B, f being (
  Morphism of A), g being Morphism of B st f in Hom(a1,a2) & g in Hom(b1,b2)
  holds [f,g] in Hom([a1,b1],[a2,b2])
proof
  let a1,a2 be Object of A, b1,b2 be Object of B, f be (Morphism of A), g be
  Morphism of B;
  assume f in Hom(a1,a2) & g in Hom(b1,b2);
  then [f,g] in [:Hom(a1,a2),Hom(b1,b2):] by ZFMISC_1:87;
  hence thesis by CAT_2:32;
end;
