Sending emails using exim4 on the domain, equal to hostname if mx record points to another host

Is there a website on VDS, it indicates the domain example.ru

$ hostname example.ru $ host example.ru example.ru has address 92.243.84.xx example.ru mail is handled by 10 mx1.example.ru. $ host mx1.example.ru mx1.example.ru has address 62.165.37.xx 

Is the exim4 mailer. When sending emails from the site (php mail()) in this domain, the emails are not getting through.

$ php -r "var_dump(mail('[email protected]', 'text mail', 'test'));" bool(true) $ sudo grep [email protected] /var/log/exim4/mainlog 2010-09-16 13:23:42 1Ow8on-0005Sb-Cu ** [email protected]: Unrouteable address 

When configuring exim4 among other things writes:

$ sudo dpkg-reconfigure exim4-config Please enter a semicolon-separated list of recipient domains for which this machine should consider itself the final destination. These domains are commonly called 'local domains'. The local hostname (example.ru) and 'localhost' are always added to the list given here. 

In General, the problem is just that how to make the local hostname is no longer involved in the list of local domains to send mail?

Background: prior To this was the usual sendmail had the same problem. Googled a lot about the same solutions. Here's one: forum.lissyara.su/viewtopic.php?f=20&t=21720 Tried to bend sendmail, nothing happened, spat, put exim4, as people in exile, but has not solved the problem.