1.NounA 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
⊢
C
{\displaystyle P,A\vdash C}
to an inference of the form
P
⊢
A
→
C
{\displaystyle P\vdash A\rightarrow C}
or vice versa, where
⊢
{\displaystyle \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."