theorem Th51:
  [[Hom(cod f,dom g),Hom(dom f,cod g)],hom(f,g)] is Element of Maps(Hom(C))
proof
A1: Hom(dom f,cod g) in Hom(C) & Hom(cod f,dom g) in Hom(C);
  Hom(dom f,cod g) = {} implies Hom(cod f,dom g) = {} by Th50;
  hence thesis by A1,Th5;
end;
