How can a logical approach help prove Boolean algebra properties?

[seang]

For my digital logic class, we are supposed to prove all of the two and three variable properties (commutative, associative, distributive...). I'm not really sure how to go about this, because although he didn't say, it seems intuitive to prove them in order, ie you can't use a property until you've proved it.

So I'm thinking about using the Single Variable Theorems for the first few (x+x = x , x*x = x , etc)

So then I started to say, for the commutative property, yx=xy, multiply each side by x to get xyx=xxy, but then, wouldn't I have to use the associatve property to group the x's together to obtain 1?, so that y=y?

Help?

 

[Hurkyl]

Well, you have to start at some definition (or list of assumed axioms) before you can prove anything; where is your starting point for + and *?