Proving Equation: m + (n + (p + q)) = ((m+n) + p) + q

[mossfan563]

Homework Statement

I have to prove this equation:
m + (n + (p + q)) = (m + n) + (p + q) = ((m + n) + p) + q

Homework Equations

Commutative property of addition and multiplication
(m+n) = (n+m), (mn) = (nm)
Associative property of addition and multplication
(m+n)+p = m+(n+p), (mn)p = m(np)
Distributive property
m * (n+p) = mn + mp

The Attempt at a Solution

Only being allowed to use certain axioms, I ruled out all except the ones in the relevant equations.
So far I'm pretty much stumped as to how to prove the equation. Going from the first part to the second is difficult. I tried to manipulate the first part of the equation to use commutative and I got nowhere. How do I get myself in the right direction?

 

[rochfor1]

You should use associativity, not commutativity.