How to get a double line subset symbol, (but not \Subset)?

I've seen the notation used in Rudin's book “Real and complex analysis”. Perhaps, simply doubling \subset is too crude. Here's a possible solution, top line is \subset\subset, bottom line \ssubset defined with some backspace between the two.

\documentclass{article}
\newcommand{\ssubset}{\subset\joinrel\subset}

\begin{document}
$A\subset\subset B$

$A\ssubset B$
\end{document}

If you want to be quite similar to \ll, then you can use this symbol, which overlaps the two \subsets. It should work properly in all sizes:

\documentclass{article}

\usepackage{mathtools}

\newcommand\ssubset{
  \mathrel{
    \mathrlap{\subset}
    \hphantom{\ll}
    \mathllap{\subset}
  }
}

\begin{document}

\[
  A\ssubset B_{A\ssubset B_{A\ssubset B}}
\]

\end{document}

In the above code I wrote it on several lines to show a bit what's going on. The one-liner works as well of course:

\newcommand\ssubset{\mathrel{\mathrlap{\subset}\hphantom{\ll}\mathllap{\subset}}}