theorem Th47:
  [[Hom(cod f,a),Hom(dom f,a)],hom(f,a)] is Element of Maps(Hom(C) )
proof
  Hom(dom f,cod f) <> {} by CAT_1:2;
  then
A1: Hom(dom f,a) = {} implies Hom(cod f,a) = {} by CAT_1:24;
  Hom(dom f,a) in Hom(C) & Hom(cod f,a) in Hom(C);
  hence thesis by A1,Th5;
end;
