PHP Authentication System

Need some expert advice,

I have a site that currently uses phpbb for authentication for the entire site (localgolfer.com).  I would like to remove phpbb from the site and find a new authentication system.

I'm trying to find a framework for user login that is the following:

-Can import my current username/passwords database, and legacy users can still login via username and password
-Easy to use a simple if statement to test if the user is logged in
-PHP based
-User stays logged in from page to page and framework handles all that
-Has social login abilities for at least Facebook, but also Twitter, etc.
-Easy to integrate with MySQL and I can add extra "profile" fields without having to deal with framework.

I have seen HybridAuth and LoginRadius, but I do not think I can import usernames and have users still login with username and password.