deduction theorem

== English == === Noun === deduction theorem (plural deduction theorems) (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 ⊢ 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. === See also === conditional proof