.htaccess - remove www from https

I'm trying to find a htaccess rewrite to remove www. from https: pages only. Every article I've found removes www for all pages.

What do I need in .htaccess to do this?

https://www.mydomain.com should be https://mydomain.com

https://mydomain.com should remain https://mydomain.com

http://www.mydomain.com should remain http://www.mydomain.com

http://mydomain.com should remain http://mydomain.com

I've been able to get the following working:

RewriteCond %{HTTPS}s ^on(s)|
RewriteCond http%1://%{HTTP_HOST}%{REQUEST_URI} ^(https?://)www\.(.+) [NC]
RewriteRule ^ %1%2 [L,R,QSA]

But this rewrites both https and http

Here is my current .htaccess

SetEnv DEFAULT_PHP_VERSION 5
RewriteEngine on
RewriteOptions MaxRedirects=1
# You may need to uncomment the following line on some hosting environments,
# for example on unitedhosting.co.uk
# RewriteBase /
# The following line has been added in order to exclude the webim
# directory from the LemonStand URL processing.
RewriteCond %{REQUEST_URI} !^/webim
#
# Do not allow executing any PHP scripts
#
RewriteRule ^(.*).php$ index.php [L]
#
# The following section automatically adds a trailing slash to all URLs
#
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_URI} !(\.[a-zA-Z0-9]{1,5}|/)$
RewriteCond %{HTTP:X-REQUESTED-WITH} !^(XMLHttpRequest)$
RewriteCond %{REQUEST_METHOD} !^HEAD$
RewriteCond %{REQUEST_METHOD} !^POST$
RewriteRule (.*)([^/])$ %{REQUEST_URI}/ [R=301,L]
# The following line has been added in order to exclude the webim
# directory from the LemonStand URL processing.
RewriteCond %{REQUEST_URI} !^/webim
#
# Product files downloading URL
#
RewriteRule (^download_product_file/.*) index.php?q=/$1 [L,QSA]
# The following line has been added in order to exclude the webim
# directory from the LemonStand URL processing.
RewriteCond %{REQUEST_URI} !^/webim
#
# Administration Area file downloading URL
#
RewriteRule ls_backend/files/get/(.*) index.php?q=/backend_file_get/$1 [L]
# The following line has been added in order to exclude the webim
# directory from the LemonStand URL processing.
RewriteCond %{REQUEST_URI} !^/webim
#
# All other requests
#
RewriteCond %{REQUEST_URI} !(\.(ico|js|jpg|gif|css|png|swf|flv|txt|xml|xls|pdf|eot|woff|ttf|svg|mp4)$)
RewriteCond %{REQUEST_URI} !(phproad/thirdpart/.*)
RewriteRule ^(.*)$ index.php?q=/$1 [L,QSA]
ErrorDocument 404 "File not found"
#
# PHP configuration
#

php_flag session.auto_start off
php_value session.cookie_lifetime 31536000
php_flag session.use_cookies on
php_flag session.use_only_cookies on
php_value session.name FWCSESSID
php_flag short_open_tag on
php_flag asp_tags on
php_flag magic_quotes_gpc off
php_value date.timezone GMT
php_value post_max_size 100M
php_value upload_max_filesize 100M
php_value memory_limit 264M