Get localized short date pattern as String?

Get localized short date pattern as String?

I'd like to get the pattern of a "short date" as a String that is
customized to the user's locale (e.g. "E dd MMM"). I can easily get a
localized DateFormat-object using
DateFormat mDateFormat =
android.text.format.DateFormat.getDateFormat(mContext);
but DateFormat doesn't have a .toPattern()-method.
If I use
SimpleDateFormat sdf = new SimpleDateFormat();
String mDateFormatString = sdf.toPattern();
I don't know how to only get the short date pattern String instead of the
full M/d/yy h:mm a