Chapter 1.6, Problem 28E

Use rules of inference to show that if $\forall x\left(P\left(x\right)\vee Q\left(x\right)\right)$ and $\forall x\left(\left(\neg P\left(x\right)\wedge Q\left(x\right)\right)\to R\left(x\right)\right)$ are true, then $\forall x\left(\neg R\left(x\right)\to P\left(x\right)\right)$ is also true, where the domains of all quantifiers are the same.