Stoker id utilisateur dans variable de ssession

<?php
session_start();
require 'Core/auth.php';
require 'Core/config.php';
if(isset($_POST) && !empty($_POST['login']) && !empty($_POST['pass'])){
extract($_POST);
$pass = sha1($pass);
mysql_connect('host','login','pass');
mysql_select_db('db');
$sql = "SELECT id FROM users WHERE pseudo='$login' AND mdp='$pass'";
$req = mysql_query($sql) or die(mysql_error());
if(mysql_num_rows($req)>0){
$_SESSION['Auth'] = array('login' => $login,'pass' => $pass,);
 header('Location:index.php');
}
else{}
}
?>

le code de auth.php:
<?php
class Auth{

  static function isLogged(){

  if(isset($_SESSION ['Auth']) && isset($_SESSION['Auth']['login']) && isset($_SESSION['Auth']['pass'])){
   return true;
  }
  else{
   return false;
  }

 }

}
?>