Why are these two applications of Bayes' Theorem equal?

[dagnir]

I'm reviewing some notes regarding probability, and the section regarding Conditional Probability gives the following example:

The middle expression is clearly just the application of Bayes' Theorem, but I can't see how the third expression is equal to the second. Can someone please clarify how the two are equal?

 

[mfb]

The numerator is P(X,Y,Z) in both cases.

 

[dagnir]

Thank you!