Baire space, analytic sets

Question

I am reading a proof from the book 'Banach spaces and descriptive set theory, lemma 7.2' and it uses the following argument: If $A\subset X$ is analytic and $X$ is a closed subspace of the Baire space $\mathcal{N}$, then $A$ can be seen as an analytic subset of $\mathcal{N}$. My question is where did this step come from?