# How to derive this conditional distribution function for a Restricted Boltzmann Machine?

I am following along Ian Goodfellow's new Deep Learning book and, reading the last chapter, I am confused about equations 20.7-20.9.

We have a joint distribution function, $P(v,h)$, and we are interested in finding the conditional distribution function, $P(h|v)$. If, from the definition of the Restricted Boltzmann Machine,

$$P(v, h) = \frac{1}{Z} \exp(b^Tv +c^Th + v^TWh)$$ where $Z$ is the normalizing constant,

$$Z = \sum_v \sum_h \exp(b^Tv +c^Th + v^TWh).$$

$P(h|v)$ is then (copied from the chapter):

\begin{align} P(h|v) &= \frac{P(h,v)}{P(v)} \tag{20.7}\\[5pt] &= \frac{1}{P(v)}\frac{1}{Z}\exp(b^Tv +c^Th + v^TWh) \tag{20.8}\\[5pt] &= \frac{1}{Z'}\exp(c^Th + v^TWh) \tag{20.9} \end{align}

That last step is where I am confused. What is $Z'$ -- there is nothing about that in the text? Is it some other constant that serves as a new normalizing constant or is it actually a derivative with respect to either $v$ or $h$? Could someone fill in some missing steps?