URL Redirection not Working for dynamic URLs

I am writing a Apache rewrite rule for following URL -

http://localhost/domain/my_directory/sub_cat.php?parent_id=56&name=Anytitle

--------to get this:-------
http://localhost/domain/my_directory/56/Anytitle


..that am successfully able rewrite it but the prob is that page is now opening for both OLD and NEW URL

I wanted to redirect my old URL to New URL i have rewrited thru this rewrite URL

Here is my mod_rewrite Code --------

RewriteEngine On
RewriteBase /my_directory/
Options +FollowSymLinks +Indexes
RewriteRule ([0-9]+)/([a-zA-Z0-9_-]+) http://localhost/domain/my_directory/sub_cat.php?parent_id=$1&name=$2 [L]
RewriteCond %{QUERY_STRING} sub_cat\.php\?parent_id=([0-9]+)&name=([a-zA-Z0-9_-]+)$ 
RewriteRule sub_cat\.php$ http://localhost/domain/my_directory/%1/%2? [R,L]

Code (markup):

I am not able to redirect the OLD URL to new URL i.e. page is now opening for both:
-http://localhost/domain/my_directory/sub_cat.php?parent_id=56&name=Anytitle
--as well as--
-http://localhost/domain/my_directory/56/Anytitle

I want this /localhost/domain/my_directory/sub_cat.php?parent_id=56&name=Anytitle to be Redirected to this -> /localhost/domain/my_directory/56/Anytitle.

Any help !..

Thx in anticipation

 

You should be fine if you replace the following line:

RewriteCond %{QUERY_STRING} sub_cat\.php\?parent_id=([0-9]+)&name=([a-zA-Z0-9_-]+)$ 

Code (markup):

with

RewriteCond %{REQUEST_URI} sub_cat\.php\?parent_id=([0-9]+)&name=([a-zA-Z0-9_-]+)$ 

Code (markup):