Rule of Idempotence/Conjunction

Theorem

The conjunction operator is idempotent:

Formulation 1

$p \dashv \vdash p \land p$

Formulation 2

$\vdash p \iff \paren {p \land p}$

Its abbreviation in a tableau proof is $\textrm{Idemp}$.

Also known as

This rule is also known as the law of tautology for logical multiplication (or conjunction).