To make sure our mail server is not used as an open relay, we will also add smtpd_recipient_restrictions to main.cf:

smtpd_recipient_restrictions =
    permit_mynetworks
    permit_sasl_authenticated 
    reject_unauth_destination
    reject_unlisted_recipient
    reject_unverified_recipient

You need to restart Postfix once again. After setting this up you should check if your mail server can be used as an open relay. If you have installed OSSEC for intrusion detection don't worry if the test don't finish because OSSECs active response blocks hosts that try to abuse your server (like the open relay test tool).