Page redirect with successful Ajax request

I have a form that uses Ajax for client-side verification. The end of the form is the following:

$.ajax({
        url: 'mail3.php',
        type: 'POST',
        data: 'contactName=' + name + '&contactEmail=' + email + '&spam=' + spam,

        success: function(result) {
            //console.log(result);
            $('#results,#errors').remove();
            $('#contactWrapper').append('<p id="results">' + result + '</p>');
            $('#loading').fadeOut(500, function() {
                $(this).remove();

            });

        }
    });

EDIT: this is my mail3.php file dealing with errors:

$errors=null; 

if ( ($name == "Name") ) {
    $errors = $nameError; // no name entered
}
if ( ($email == "E-mail address") ) {
    $errors .= $emailError; // no email address entered
}
if ( !(preg_match($match,$email)) ) {
    $errors .= $invalidEmailError; // checks validity of email
}
if ( $spam != "10" ) {
    $errors .= $spamError; // spam error
}

if ( !($errors) ) {
    mail ($to, $subject, $message, $headers);
    //header ("Location: thankyou.html");
    echo "Your message was successfully sent!";
    //instead of echoing this message, I want a page redirect to thankyou.html

} else {
    echo "<p id='errors'>";
    echo $errors;
    echo "</p>";
}

I was wondering if it's possible to redirect the user to a Thank You page if the ajax request is successful and no errors are present. Is this possible?

Thanks! Amit