reactivate a checkbox in a dynamic list jquery

I'm trying to reactivate a checkbox in a dynamic list and I do not succeed, the list update its contents every x time.

<div class="content">
    <ul class="mylist">
        <li><input type="checkbox" class="check" checked>0</li>
        <li><input type="checkbox" class="check">1</li>
        <li><input type="checkbox" class="check">2</li>
        <li><input type="checkbox" class="check">3</li>
        <li><input type="checkbox" class="check">4</li>
        <li><input type="checkbox" class="check">5</li>
        <li><input type="checkbox" class="check">6</li>
        <li><input type="checkbox" class="check">7</li>
    </ul>
</div>
// checkbox 
var checkbox;
var list = [2,3,4,5,6,7,8,9];
//
setInterval(function(){
    $('.mylist li').remove();
    for(i in list) {
        $('.mylist').append('<li><input type="checkbox" class="check">' + i + '</li>');
    }
    if(typeof checkbox === 'object')
        checkbox.prop('checked', true);
}, 3000);

$('.check').on('click', function(){
  if ($(this).is(":checked")) {
     checkbox = $(this);
 }
});

http://ift.tt/2vSTCA3