reserve X for set;
reserve UN for Universe;

theorem
  for u,v being Element of UN holds
  Funcs(u,v) c= the set of all f where f is Function of u,v
  proof
    let u,v be Element of UN;
    set F = the set of all f where f is Function of u,v;
    now
      let o be object;
      assume o in Funcs(u,v);
      then consider f be Function such that
A1:   o = f and
A2:   dom f = u and
A3:   rng f c= v by FUNCT_2:def 2;
      reconsider f as Function of u,v by A2,A3,FUNCT_2:2;
      f in F;
      hence o in F by A1;
    end;
    hence thesis;
  end;
