If you are a member of one of (some of) the national healthcare systems in Europe you are also covered in many other European countries (not just the EU) as if

If you are a member of one of (some of) the national healthcare systems in Europe you are also covered in many other European countries (not just the EU) as if you were part of their system, even when you're just a tourist. (The back of your card in Germany has the international information.)