reserve V for non empty set,
  A,B,A9,B9 for Element of V;

theorem Th1:
  for f being set holds f in Funcs(V) iff ex A,B st (B={} implies A
  ={}) & f is Function of A,B
proof
  let f be set;
  set F = the set of all  Funcs(A,B);
  thus f in Funcs(V) implies ex A,B st (B={} implies A={}) & f is Function of
  A,B
  proof
    assume f in Funcs(V);
    then consider C being set such that
A1: f in C and
A2: C in F by TARSKI:def 4;
    consider A,B such that
A3: C = Funcs(A,B) by A2;
    take A,B;
    thus thesis by A1,A3,FUNCT_2:66;
  end;
  given A,B such that
A4: ( B={} implies A={})& f is Function of A,B;
A5: Funcs(A,B) in F;
  f in Funcs(A,B) by A4,FUNCT_2:8;
  hence thesis by A5,TARSKI:def 4;
end;
