PokéBase - Pokémon Q&A
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The games have been stated to include every Pokémon that was featured in the original Diamond and Pearl (493 Pokémon in the first four generations)

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According to Bulbapedia, BDSP only includes the first 493 Pokemon, which means Sylveon is not one of those and hence unobtainable.

Hope this helps.

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Sad =[ thanks anyways!
Happy to help.