# Conjunction introduction

Conjunction introduction (often abbreviated simply as conjunction and also called and introduction)[1][2][3] 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:

${\displaystyle {\frac {P,Q}{\therefore P\land Q}}}$

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

## Formal notation

The conjunction introduction rule may be written in sequent notation:

${\displaystyle P,Q\vdash P\land Q}$

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

where ${\displaystyle P}$ and ${\displaystyle Q}$ are propositions expressed in some formal system.

## References

1. ^ Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing. pp. 346–51.
2. ^ Copi and Cohen
3. ^ Moore and Parker