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

theorem Th23:
  for A,B,C being set st C = {} implies B = {} or A = {}
  for f being Function of A, Funcs(B,C) holds
    Frege f is Function of Funcs(A,B), Funcs(A,C)
proof
  let A,B,C be set;
  assume
A1: C = {} implies B = {} or A = {}; then
A2: Funcs(A,C) = {} implies Funcs(A,B) = {} by FUNCT_2:8;
  let f be Function of A, Funcs(B,C);
  dom Frege f = Funcs(A,B) & rng Frege f c= Funcs(A,C) by A1,Th21,Th22;
  hence thesis by A2,FUNCT_2:def 1,RELSET_1:4;
end;
