As you can see from the image below, how does Px,z(x,z) change to Px,y(z-x)? Can someone tell me the logic behind it or, refer me to a link that talks about the similar topic? Thanks alot!!
Note that $Z=X+Y$. So we have $(X,Z)=(x,z)$ if and only if $(X,X+Y)=(x,z)$. But $X=x$ and $X+Y=z$ iff $X=x$ and $Y=z-x$.