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 Th4:
  ex f,A,B st m = [[A,B],f] & (B = {} implies A = {}) & f is Function of A,B
proof
  m in { [[A,B],f]: (B={} implies A={}) & f is Function of A,B};
  then ex A,B,f st m = [[A,B],f] & (B={} implies A={}) & f is Function of A,B;
  hence thesis;
end;
