Ho provato a correggere in questo modo, ma non cambia niente, anzi colleziono due variabili indefinite in più:

Codice PHP:
class login extends registrati{
    public 
$nickname;
    protected 
$password;
    protected 
$num_rows;
    protected 
$assoc;
    
    public function 
__construct(){
        
parent ::__construct();
        
$this->nickname=mysql_real_escape_string($_POST['nickname']);
        
$this->password=mysql_real_escape_string($_POST['password']);
        
$this->query="SELECT * FROM utenti WHERE nickname='{$this->nickname}' AND password='{$this->password}'";
        
$this->result=mysql_query($this->query$this->conn);
        
$this->num_rows=@mysql_num_rows($this->result);
        
$this->assoc=mysql_fetch_assoc($this->result);
    }