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If you are an EU national, you do not need to show your national ID card or passport when you are travelling from one border-free Schengen EU country to another.
Even if you don't need a passport for border checks within the Schengen area , it is still always highly recommended to take a passport or ID card with you, so you can prove your identity if needed (if stopped by police, boarding a plane, etc.). Schengen EU countries have the possibility of adopting national rules obliging you to hold or carry papers and documents when you are present on their territory.
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