Array
(
    [user_mob_1] => Array
        (
            [mob_code] => 06
            [mob] => 069633345
            [type] => 1
            [phone_id] =&         
        
Your idea of using a built-in function like array_filter is a very good one; PHP has lots of these that can make your life easier.
Specifically, array_filter accepts a callback that you can use to customize the filtering logic. This would work:
$filtered = array_filter($array, function($el) { return !empty($el['mob']); });
Here the callback is supplied as an anonymous function.