Simplify this Boolean Expression

A & ~((~A) & (~B)).

According to the truth table I did it should be equivalent to ~B but I can't get the boolean algebra to work out to that.

A & ~((~A) & (~B))

= A & (~~A or ~~B) Demorgan's law

= A & (A or B) Double negation

= (A & A) or (A & B) Distributive Property

And this is where I get stuck. If A&A = just A then you get into an infinate loop of distrubutive properties and never reach your goal.