Chapter 1.6, Problem 26E

Justify the rule ofuniversal transitivity, which states that if $\forall x\left(P\left(x\right)\to Q\left(x\right)\right)$ and $\forall x\left(Q\left(x\right)\to R\left(x\right)\right)$ are true, then $\forall x\left(P\left(x\right)\to R\left(x\right)\right)$ is true, where the domains of all quantifiers are the same.