theorem Th50:
  Hom(dom f,cod f9) = {} implies Hom(cod f,dom f9) = {}
proof
  assume that
A1: Hom(dom f,cod f9) = {} and
A2: Hom(cod f,dom f9) <> {};
A3: Hom(dom f9,cod f9) <> {} by CAT_1:2;
  Hom(dom f,cod f) <> {} by CAT_1:2;
  then Hom(dom f,dom f9) <> {} by A2,CAT_1:24;
  hence contradiction by A1,A3,CAT_1:24;
end;
