Redirect wordpress subdomain fails with /admin

Question

I have a wordpress installed in my public_html under the foo.com domain. I've installed a new wordpress site under public_html/bar under the bar.com domain. I have the following htaccess files:

public_html:

<IfModule mod_rewrite.c>
RewriteEngine on
RewriteCond %{HTTP_HOST} ^(www.)?bar.com$
RewriteCond %{REQUEST_URI} !^/bar/
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ /bar/$1
RewriteCond %{HTTP_HOST} ^(www.)?bar.com$
RewriteRule ^(/)?$ bar/index.php [L]
</IfModule>

When I tried to enter to bar.com, the site displays correctly. But when I try to enter bar.com/admin the site redirects me to foo.com/wp-login. Is there any additional config tha I'm missing?