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Conjunction introduction : ウィキペディア英語版
Conjunction introduction

Conjunction introduction (often abbreviated simply as conjunction and also called and introduction〔Copi and Cohen〕〔Moore and Parker〕) is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof. It is the inference that if the proposition ''p'' is true, and proposition ''q'' is true, then the logical conjunction of the two propositions ''p and q'' is true. For example, if it's true that it's raining, and it's true that I'm inside, then it's true that "it's raining and I'm inside". The rule can be stated:
:\frac
where the rule is that wherever an instance of "P" and "Q" appear on lines of a proof, a "P \and Q" can be placed on a subsequent line.
== Formal notation ==
The ''conjunction introduction'' rule may be written in sequent notation:
: P, Q \vdash P \and Q
where \vdash is a metalogical symbol meaning that P \and Q is a syntactic consequence if P and Q are each on lines of a proof in some logical system;
where P and Q 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)
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