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 Th5:
  for f being Function of A,B st B={} implies A={} holds [[A,B],f] in Maps V
proof
  let f be Function of A,B;
  assume
A1: B = {} implies A = {};
  then f in Funcs(V) by Th1;
  hence thesis by A1;
end;
