reserve X for set;
reserve UN for Universe;

theorem
  for UN being Universe, V being non empty Element of UN
  holds Funcs(V) is Subset of UN
  proof
    let UN be Universe;
    let V be non empty Element of UN;
    now
      let o be object;
      assume o in the set of all Funcs(A,B) where A,B is Element of V;
      then consider A,B be Element of V such that
A1:   o = Funcs(A,B);
A2:   UN is axiom_GU1;
      reconsider A,B as Element of UN by A2;
      Funcs(A,B) in UN;
      hence o in UN by A1;
    end;
    then the set of all Funcs(A,B) where A,B is Element of V c= UN;
    then union the set of all Funcs(A,B) where A,B is Element of V c= union UN
      by ZFMISC_1:77;
    hence thesis by Th81;
  end;
