deduction theorem

Noun

 * 1)  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.