How to make one case equation point to another case equation?

Question

I want to display the following

I'm trying to realize it with the following code

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
        \begin{equation}
                    \begin{cases}
             &a + b\
             & b + c
            \end{cases} \implies
        \begin{cases}
        & c + d\\
        & d + e
        \end{cases} 
    \end{equation}

\end{document}

But this gives me a lot of errors and the wrong output

Does anyone know how to fix this?

Answer 1

In addition to getting rid of the blank line between the two cases environments, you should also (a) get rid of the & alignment operators (since you're not really making use of much of the cases machinery) and (b) insert a \quad directive after \implies in order to even out the spacing to the left and right of the \implies (aka \Longrightarrow) symbol.

\documentclass{article}
\usepackage{mathtools} % mathtools loads amsmath automatically
\begin{document}
    \begin{equation}
         \begin{cases}
            a + b\\
            b + c
         \end{cases} 
         \implies \quad
         \begin{cases}
            c + d\\
            d + e
        \end{cases} 
    \end{equation}


\end{document}