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;

theorem Th15:
  for f being Function of A,B st B = {} implies A = {} holds [[A,B
  ],f] in Maps(A,B)
proof
  let f be Function of A,B;
  assume B = {} implies A = {};
  then f in Funcs(V) & [[A,B],f] in Maps(V) by Th1,Th5;
  hence thesis;
end;
