The proof of a theorem about an elliptic function.

Question

I'm studying The Arithmetic of Elliptic Curves by Joseph H.Silverman. In the section VI(Elliptic Curves over $\mathbb{C}$) , the following theorem is;

Let $\mathbb{\Lambda}$ be a lattice.Then \begin{equation} \mathbb{C}(\mathbb{\Lambda}) = \mathbb{C}(\wp(z),\wp^\prime (z)), \end{equation} where $\mathbb{C}(\Lambda)$ is the set of elliptic functions relative to the lattice $\Lambda$ , $\wp (z)$ is the Weierstrass $\wp$-function relative to the lattice $\Lambda$.

I have a quetion about the beginning of the proof.

Proof.

Let $f(z) \in \mathbb{C}(\Lambda)$.Writing \begin{equation} f(z) = \dfrac{f(z)+f(-z)}{2} + \dfrac{f(z)-f(-z)}{2}, \end{equation} we see that it suffices to prove the theorem for functions that are either odd or even.

I don't know why it is sufficient. I'm sorry for the basic question.