PHP Unset Command in If Statement Not Working

Your unsetting $keylist not $_POST

unset($_POST["keys"]);

You're using the wrong array key for unsetting (You're trying to unset $keylist["HHH"], not, say, $keylist[0]) - you'll need to retrieve the key from the array, and then unset that specifically in order to remove it from the keylist.

$index = array_search($_POST["keys"], $keylist);
if($index!==false) { //YES, NOT DOUBLE EQUALS
    unset($keylist[$index));
}

If $_POST["keys"] is an array of keys, you'll need to use array_keys with a search_value instead.

Array_search documentation: http://php.net/manual/en/function.array-search.php

Array_keys documentation: http://php.net/manual/en/function.array-keys.php

EDIT: Adding a full, working example.

<?
$_POST["keys"]="asdjkgldshglsjhgsdlhgsdlghsdlghsdlgh";
$keylist=array("asdjkgldshglsjhgsdlhgsdlghsdlghsdlgh","derp2");
if(in_array($_POST["keys"], $keylist)) {
    $indexToRemove = array_search($_POST["keys"], $keylist);
    echo "1";
    print_r($keylist);
    unset($keylist[$indexToRemove]);
    print_r($keylist);
} else {
    echo "0";
    print_r($keylist);
}
?>

Another example, this time checking the index itself to see if it is not false:

<?
$_POST["keys"]="asdjkgldshglsjhgsdlhgsdlghsdlghsdlgh";
$keylist=array("asdjkgldshglsjhgsdlhgsdlghsdlghsdlgh","derp2");
$indexToRemove = array_search($_POST["keys"], $keylist);
if($indexToRemove!==false) {
    echo "1";
    print_r($keylist);
    unset($keylist[$indexToRemove]);
    print_r($keylist);
} else {
    echo "0";
    print_r($keylist);
}
?>

Output:

1Array ( [0] => asdjkgldshglsjhgsdlhgsdlghsdlghsdlgh [1] => derp2 ) Array ( [1] => derp2 )

I realize now that I only had one = on the $index!==false check - the reason you need two is because $index is 0 if you're removing the first element of an array. Per PHP documentation,

Warning
This function may return Boolean FALSE, but may also return a non-Boolean
value which evaluates to FALSE. Please read the section on Booleans for more 
information. Use the === operator for testing the return value of this function.

in_array($_POST["keys"], $keylist) checks if the posted value $_POST["keys"] is present as a value in $keylist, but unset($keylist[$_POST["keys"]]) uses $_POST["keys"] as the key in $keylist to unset something.

Since in_array() returns true, the posted value is present in the array $keylist. But you can't do unset($keylist['GGG']) because that value is not set.

A simple solution is to use the same values as keys too:

$keylist = array('HHH', 'GGG');
$keylist = array_combine($keylist, $keylist);

More about array_combine().

Your array have keys. So "HHH" in keylist is $keylist[0] and not $keylist['HHH']. You can not unset it because you have to define the array key instead of the array value. Try to search for the array value like this:

array_search($_POST["keys"], $keylist)

This will return the array key for you or false if its not found. Your full code should like look like:

echo "1"; 
$arrkey = array_search($_POST["keys"], $keylist);
if( $arrkey !== false ){
unset($keylist[$arrkey]);
}

Here the PHP Manual for the array_search function: http://php.net/manual/en/function.array-search.php