# For all

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If is a predicate that depends on , then "for all , " is a proposition. It is true if every possible value of makes evaluate to true.

The fact that is arbitrary does not mean you get to pick ; on the contrary, your proof should work no matter what you choose. This means you can't use any property of other than that .

• If you know holds for all , then you can conclude holds for any specific . For example, if you know for all , , then you can conclude (since ).