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 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;
