Nat Deduction Proof - Distributive property I need to prove (P v Q) ^ (P v R) |- P v (Q ^ R) using natural deduction and propositional logic.  I should be able to do it using only AND and OR rules, but I am stuck on how to assume Q and R.  This is what I have:
(P v Q) ^ (P v R)________premise
P v Q________________^e1___1
P v R________________^e2___1
...P__________________assumption
...P v (Q ^ R)___________vi1___4
I know this is right so far.  I just don't know how to introduce my assumptions for Q and R.  Do I assume ~P?  If so, which rule is applied, and what is the process, to conclude Q ^ R?  Thanks for any help you can give me

Assume $\rm \neg P$, then from 2 and 3 derive $\rm Q$ and $\rm R$. From that you have $\rm Q\wedge R$, and so on...
The rule, $\rm \neg P,\, P\vee Q \,\vdash\, Q$ , is called Deductive Syllogism.  Sometimes also known as disjunctive elimination ($\rm\vee e$), or historically as modus tollendo ponens.
