Rule of Idempotence

Definition
The rule of idempotence is two-fold:


 * Conjunction is idempotent:
 * $$p \dashv \vdash p \and p$$


 * Disjunction is idempotent:
 * $$p \dashv \vdash p \or p$$

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

Proof by Natural deduction
These are proved by the Tableau method.

Proof by Truth Table
Let $$v: \left\{{p}\right\} \to \left\{{T, F}\right\}$$ be an interpretation for a boolean variable $$p$$.