Conjunction introduction

Conjunction introduction is a valid rule of inference of propositional logic. It makes it possible to introduce a conjunction into a logical proof. If p is true, and q is true, then the logical conjunction 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".

Formally:

$p\,\!$

${\frac {q\,\!\qquad \quad }{}}$

$(p\wedge q)$

Proof

Proposition	Derivation
$P\,\!$	Given
$Q\,\!$	Given
$\neg P\lor Q$	Addition
$P\rightarrow Q$	Material implication
$P\rightarrow (P\land Q)$	Absorption
$P\land Q$	Modus ponens