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In propositional logic, conjunction elimination (also called ''and'' elimination, ∧ elimination,〔 Sect.3.1.2.1, p.46〕 or simplification)〔Copi and Cohen〕〔Moore and Parker〕〔Hurley〕 is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction ''A and B'' is true, then ''A'' is true, and ''B'' is true. The rule makes it possible to shorten longer proofs by deriving one of the conjuncts of a conjunction on a line by itself. An example in English: :It's raining and it's pouring. :Therefore it's raining. The rule consists of two separate sub-rules, which can be expressed in formal language as: : and : The two sub-rules together mean that, whenever an instance of "" appears on a line of a proof, either "" or "" can be placed on a subsequent line by itself. The above example in English is an application of the first sub-rule. == Formal notation == The ''conjunction elimination'' sub-rules may be written in sequent notation: : and : where is a metalogical symbol meaning that is a syntactic consequence of and is also a syntactic consequence of in logical system; and expressed as truth-functional tautologies or theorems of propositional logic: : and : where and are propositions expressed in some formal system. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「conjunction elimination」の詳細全文を読む スポンサード リンク
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