reserve V for non empty set,
  A,B,A9,B9 for Element of V;
reserve f,f9 for Element of Funcs(V);
reserve m,m1,m2,m3,m9 for Element of Maps V;
reserve a,b for Object of Ens(V);
reserve f,g,f1,f2 for Morphism of Ens(V);
reserve C for Category,
  a,b,a9,b9,c for Object of C,
  f,g,h,f9,g9 for Morphism of C;

theorem
  (Hom(a,cod f) = {} implies Hom(a,dom f) = {}) & (Hom(dom f,a) = {}
  implies Hom(cod f,a) = {})
proof
  Hom(dom f,cod f) <> {} by CAT_1:2;
  hence thesis by CAT_1:24;
end;
