theorem Th46:
  [[Hom(a,dom f),Hom(a,cod f)],hom(a,f)] is Element of Maps(Hom(C) )
proof
  Hom(dom f,cod f) <> {} by CAT_1:2;
  then
A1: Hom(a,cod f) = {} implies Hom(a,dom f) = {} by CAT_1:24;
  Hom(a,dom f) in Hom(C) & Hom(a,cod f) in Hom(C);
  hence thesis by A1,Th5;
end;
