reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem
  for V, C being non empty set ex f be Element of PFuncs (V, C) st f <> {}
proof
  let V, C be non empty set;
  consider a be object such that
A1: a in V by XBOOLE_0:def 1;
  consider b be object such that
A2: b in C by XBOOLE_0:def 1;
  set f = {[a,b]};
  {a} c= V by A1,ZFMISC_1:31;
  then
A3: dom f c= V by RELAT_1:9;
  {b} c= C by A2,ZFMISC_1:31;
  then rng f c= C by RELAT_1:9;
  then reconsider f as Element of PFuncs (V, C) by A3,PARTFUN1:def 3;
  f <> {};
  hence thesis;
end;
