# Conjunction introduction

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Conjunction introduction (often abbreviated simply as conjunction and also called and introduction) 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:

${\frac {P,Q}{\therefore P\land Q}}$ where the rule is that wherever an instance of "$P$ " and "$Q$ " appear on lines of a proof, a "$P\land Q$ " can be placed on a subsequent line.

## Formal notation

The conjunction introduction rule may be written in sequent notation:

$P,Q\vdash P\land Q$ where $P$ and $Q$ are propositions expressed in some formal system, and $\vdash$ is a metalogical symbol meaning that $P\land Q$ is a syntactic consequence if $P$ and $Q$ are each on lines of a proof in some logical system;