Can't send mails with mail() function

So, okay. I found the problem. For anyone wh might have the same trouble, here is solution.
My server's php was configured to send mails already with the "-f" flag in php.ini.
So it was:
sendmail_path = /usr/sbin/sendmail -t -i -f [email protected]

Just remove -f [email protected] so it will look like "sendmail_path = /usr/sbin/sendmail -t -i" and enjoy!