# Rule of Idempotence/Conjunction

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## 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**).