Laravel query from collection

I'm trying to filter Members who have Groups that are of a different type through the relations. I want it to filter it to only those Members, but instead it seems to still return all members of that type. This is the code I've been using:

$members = Member::where('type', 1)->with(['groups' => function ($query) {
      $query->where('type', 0);}])->get();

What I want is something like this (although this generates an error):

$members = Member::where('type', 1)->where(['groups' => function ($query) {
      $query->where('type', 0);}])->get();

Is there a different approach I could use do this?

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