Prove A.(B+C) = (A.B)+(A.C) <Boolean Algebra>

[Valour549]

Most of the results on google happily prove A+(B.C) = (A+B).(A+C), which is that OR is distributive (over AND).

But as part of their proof, they use the law that AND is distributive (over OR), namely that
A.(B+C) = (A.B)+(A.C) which I can't seem to find any algebraic proof for.

So are there any ways to prove this law without using a truth table or venn diagram?

 

[micromass]

What are the axioms you start with?