# Why does the substitution {x/f(y), y/z} work this way?

There is an example of applying a substitution to an expression, and I am having a problem with it. Let $$\theta = \{ x/f(y), y/z \}$$, and $$E=p(x,y,g(z))$$, then $$E\theta = p( f(y),z,g(z) )$$.

Why is $$y/z$$ not applied to $$E$$ after using $$x/f(y)$$, so that the answer would be $$E\theta = p( f(z),z,g(z) )$$?