# Grammar with same variables

If a grammar has the same variable multiple times, is it the same as adding a $$\mid$$ between them? For example, is

\begin{align*}S &\to bB \\ S &\to \varepsilon \\ B &\to cB \\ B &\to \varepsilon \end{align*}

equal to the following?

\begin{align*}S &\to bB \mid \varepsilon \\ B &\to cB \mid \varepsilon \\ \end{align*}

Yes. (you are right, the "$$\mid$$" sign is a classical notation for the alternative rules for a variable.)