Deduction Theorem
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High Quality Content by WIKIPEDIA articles! In mathematical logic, the deduction theorem is a metatheorem of first-order logic.] It is a formalization of the common proof technique in which an implication A B is proved by assuming A and then proving B from this assumption.The deduction theorem holds for all first-order theories with the usual deductive systems for first-order logic. However, there are first-order systems in which new inference rules are added for which the deduction theorem fails.

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High Quality Content by WIKIPEDIA articles! In mathematical logic, the deduction theorem is a metatheorem of first-order logic.] It is a formalization of the common proof technique in which an implication A B is proved by assuming A and then proving B from this assumption.The deduction theorem holds for all first-order theories with the usual deductive systems for first-order logic. However, there are first-order systems in which new inference rules are added for which the deduction theorem fails.