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 coming, and it's true that I'm inside, then it's true that "it's coming and I'm inside". The rule can be stated:

where the rule is that wherever an instance of "" and "" appear on lines of a proof, a "" can be placed on a subsequent line.

Formal notation

The conjunction introduction rule may be written in sequent notation:

where is a metalogical symbol meaning that is a syntactic consequence if and are each on lines of a proof in some logical system;

where and are propositions expressed in some formal system.


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