redirect www to non www in subfolder

I have joomla installed on root folder and another joomla installed on subfolder. I want to redirect www to non in subfolder by this code in blog htaccess:

RewriteCond %{HTTP_HOST} ^(www\.mydomain\.com)?$
RewriteRule ^(.*)$ http://mydomain.com/blog/$2 [R=301,L]

Code (markup):

it worked for root redirect but when i want browse internal page it redirect the page to home page. What is problem?

 

I used this generator: http://www.scriptalicious.com/tools/www-redirect-generator/

and it returned:

RewriteEngine On
RewriteCond %{HTTP_HOST} ^www.domain.com/blog [NC]
RewriteRule ^(.*)$ http://domain.com/blog/$1 [L,R=301]

Code (markup):

 

This code just work for root forwarding and not for internal pages

 

You can have it like this:

RewriteEngine on

RewriteCond %{HTTP_HOST} ^www\.(domain\.com)$ [NC]
RewriteRule ^ http://%1%{REQUEST_URI} [L,R=301]

RewriteCond %{HTTP_HOST} ^domain\.com$
RewriteCond %{REQUEST_URI} !^/subfolder/
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ /subfolder/$1 [L]

RewriteCond %{HTTP_HOST} ^domain\.com$
RewriteRule ^(/)?$ /subfolder/index.php [L]

Code (markup):