.htaccess rewrite to simultaneously change domain and remove path - apache

Question

My URL structure is currently as follows:
http://domain.com/folder/filename (CURRENT)
I want to change this so that I can use the following URL instead:
http://sub.domain.com/filename (NEW)
So accessing the CURRENT or the NEW url, should load the file located at the CURRENT url, but show the NEW url in the address bar. It should only apply to the "/folder/" path.
sub.domain.com is a mirror of domain.com, ie. they share the same file system and root directory.
This is what I have so far:
Options +FollowSymLinks
RewriteBase /
RewriteCond %{HTTP_HOST} ^(www.)?domain.com$ [NC]
RewriteCond %{REQUEST_URI} ^/folder/?(.*)$ [NC]
RewriteRule ^(.*)$ http://sub.domain.com/$1 [R=301,L]
This is working, but is missing the rule to remove the "/folder/" from the path. I've tried combining multiple RewriteRule's with no luck. Any ideas? Thanks.
UPDATE: Thanks again #Gerben - I understand what your rules are doing now, but the second one isn't working for me. I suspect because it's conflicting with some other rewrite rules, in particular those of WordPress, which are lower down in my .htaccess file:
# BEGIN WordPress
RewriteRule ^index\.php$ - [L]
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
# END WordPress
Because of this the page ends up in a redirect loop, ie (from Chrome):
"The webpage at http://sub.domain.com/folder/index.php has resulted in too many redirects." - while the url I was originally trying to access was, for example, http://sub.domain.com/page
Any ideas?

Answer 1

Try:
RewriteCond %{HTTP_HOST} ^(www.)?domain.com$ [NC]
RewriteRule ^(folder/)?(.*)$ http://sub.domain.com/$2 [R=301,L]
This will redirect everything to sub.domain.com, and remove the /folder part of the URI if it is there. If not, it redirects and leaves the URI untouched.

Answer 2

RewriteCond %{THE_REQUEST} /folder/
RewriteRule ^folder/(.*)$ http://sub.domain.com/$1 [R=301,L]
RewriteCond %{HTTP_HOST} ^sub\.domain\.com$ [NC]
RewriteCond %{REQUEST_URI} !^/folder/
RewriteRule ^(.*)$ folder/$1 [L]
# WordPress rules here
edit the second R=301 should not have been there
But this won't work, as wordpress has no way of knowing you want folder. You could add the Proxy flag to the rewrite, but then you need to change the rule above to not redirect on this internal proxy request.