Thank you soooooooo muchhhhh Captainblack. Without you, I won't be able to prove these laws of algebra. I have ONE LAST prove I can't prove. Will you pleaseeee helpp me on this one too? The axioms are still needed to prove this problem as well.

For every natural number i, for every natural number j, for every natural number k, i(j + k) = ij + ik.