I want to create a Context-Free grammar that generates the language

$ $ L = \{ w \in \{0, 1\}^* |\ \text{number of $ 0$ ‘s is even, and number of $ 1$ ‘s is also even} \}. $ $

I came up with

$ $ S \rightarrow 0S0S\ |\ 1S1S\ |\ ABABS\ |\ BABAS\ |\ \epsilon \ A \rightarrow 0A0A\ |\ 1A1A\ |\ 0\ B \rightarrow 0B0B\ |\ 1B1B\ |\ 1\ $ $

Looks like it does the job, but how can I be sure that it does indeed generate L.

Any help would be appreciated.