Symbolic Logic Proof of Associativity I am currently a math student in cal $b$. I know a super intelligent person that is trying to teach me symbolic logic. We've been doing okay until we've hit associativity. My "teacher" (the intelligent one) said it wasn't proved in his class and he's never seen a proof for it (that doesn't use demorgans laws). I'd love to see a proof without using DeMorgan's laws.  
So If anyone knows it here's what I'd like to see. 
Prove $pv(qvr)\Rightarrow(pvq)vr$ 
I have most of the basic theorems and such including commutivity and the contrapositive proved, but no DeMorgan's.   
Thanks guys, Have fun!! 

To prove $p\lor(q\lor r)$ implies $(p\lor q)\lor r$, assume $p\lor(q\lor r)$ is true, and then, using that assumption, show that $(p\lor q)\lor r$ is true.

Thus, assume $p\lor(q\lor r)$ is true.

Then $p$ is true, or $q \lor r$ is true.

Suppose first that $p$ is true.

Then the truth of $p$ implies the truth of $p \lor q$, which in turn implies the truth of $(p\lor q)\lor r$, as required, so this case is done.
Next suppose $q \lor r$ is true.

Consider two subcases ...

Suppose first that $q\,$ is true 

Can you finish it?
