# deduction theorem

(redirected from Deduction metatheorem)

## deduction theorem

n
(Logic) logic the property of many formal systems that the conditional derived from a valid argument by taking the conjunction of the premises as antecedent and the conclusion as consequent is true
References in periodicals archive ?
I present the metalogical results that show the property of satisfying Modus Ponens as a necessary and sufficient condition for the extended completeness of the system, and to the Deduction Metatheorem as a necessary and sufficient condition for the extended correctness of the system.
The inverse metalogical implication, known as the Deduction Metatheorem, is a very special property of an axiomatic system S.
Observe that the Deduction Metatheorem states that a conditional is derivable from a set of formulas, if its consequent is derivable from the set of formulas augmented with the antecedent.
The discovery of these general relations helped us to find that a direct way of proving the extended correctness and the extended completeness of a particular system that satisfies restricted correctness and completeness, had to be by proving that the system satisfies both Modus Ponens and the Deduction Metatheorem.
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