PHP Session Delete

I am using the below code on my log out page.

<?php
session_start();
session_destroy();
?>

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It does work and when I visit pages that require a login it doesn't allow me in which is good, but when I go to view my view my browser cookies I still see a "PHPSESSID" cookie. Why is this? Why doesn't this session cookie get deleted from my browser?

I have also output the session and it is empty.

print_r($_SESSION);

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So overall it is working. Just curious why the actual cookie does not get removed from my browser. My browser is chrome if that makes any difference.