reserve n for Element of NAT,
  p,q,r,s for Element of HP-WFF;

theorem Th21:
  for A,B,C being set st C = {} implies B = {} or A = {}
  for f being Function of A, Funcs(B,C) holds dom Frege f = Funcs(A,B)
proof
  let A,B,C be set such that
A1: C = {} implies B = {} or A = {};
  let f be Function of A, Funcs(B,C);
  thus dom Frege f = product doms f by PARTFUN1:def 2
    .= product(A --> B) by A1,Th5
    .= Funcs(A,B) by CARD_3:11;
end;
