Congratulations!!! It is always so wonderful when your pup learns something new, and play biting is one of the most difficult behaviours to correct (IMHO). It took about a year to break Leo of it.

Keep up the good work. And continue to work with him. Establishing yourself as alpha will continue as long as you keep working on his basic commands. Use the Nothing in life is free (NILIF) program. It works wonders. Make him do a required command for everything good. Make him sit before you feed him, make him sit before you take him outside, make him sit/down before you play with him. HE HAS TO DO HIS CHORES BEFORE HE CAN PLAY!!! The worst punishment you can give a dog is to ignore him, so if he gets obnoxious - walk away, turn your back or completely ignore him.

Leo had a major jumping problem when I first got him. I tried all different things until I was totally at a loss. Finally what I did that worked was when I walked in the door and he jumped on me - I would walk out the door again. I would wait outside for about 5 minutes and walk in again. If he did it again - I would leave again. It took about 2 days for him to get the idea that jumping meant no attention and that is exactly what he didn't want.

And contrary to popular belief - dogs do not want to assume the alpha roll - it is too stressful. They would much prefer to take a secondary roll.

Just my 2 cents.