deduction theorem

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deduction theorem ‎(plural deduction theorems)

  1. (logic) A procedure for "discharging" assumptions from an inference, causing them to become antecedents of the conclusion; or vice versa. Symbolically, the conversion of an inference of the form  P, A \vdash C to an inference of the form  P \vdash A \rightarrow C or vice versa, where \vdash is the turnstile symbol. The validity of the procedure is a metatheorem of the given logical theory.
    The deduction theorem reveals the relationship between logical entailment and material implication: it allows to one to "pack" or "record" an inference into a tautology, and conversely, to "unpack" or "play back" a tautology as an inference process.

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