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The Infernal Legacy racial trait grants a Tiefling the ability to cast Hellish Rebuke as a 2nd level spell and the Handbook says that you use Charisma for the spellcasting ability of these spells. So if my Ranger Tiefling has a Charisma score of 14, would the Spell Save DC for Hellish Rebuke's damage be 10 (8+Charisma Mod of 2) or would I add the proficiency bonus to it as well?

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The Spell save DC would include the proficiency bonus.

Player Handbook (p.205)

The DC to resist one of your spells equals 8 + your spellcasting ability modifier + your proficiency bonus + any special modifiers

A special modifier would be a bonus from a magic item for example.

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