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Dragon Magic Sorcerer have the following class feature:

Dragon Soul: Choose a damage type: acid, cold, fire, lightning, poison, or thunder. You gain resist 5 to that damage type. The resistance increases to 10 at 11th level and 15 at 21st level. Your arcane powers ignore any target's resistance to that damage type up to the value of your resistance.

If your resistance is increased, say by having a Book Imp familiar (You gain resist fire 5. If you already have resist fire, increase your resistance by 2), does this increase the amount of resistance you can ignore?

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YES

It says "up to the value of your resistance" and doesn't specify any qualifications about the source of that resistance, so you would ignore resist fire up to 7 in your example.

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