# Rule of Idempotence

## Theorem

The rule of idempotence is two-fold:

### Conjunction

$p \dashv \vdash p \land p$

### Disjunction

$p \dashv \vdash p \lor p$

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

## Also known as

Some sources give this as the rule of tautology or law of tautology, but this is discouraged so as to avoid confusion with the definition of tautology.

## Technical Note

When invoking Rule of Idempotence in a tableau proof, use the {{Idempotence}} template:

{{Idempotence|line|pool|statement|depends|type}}

where:

line is the number of the line on the tableau proof where Rule of Idempotence is to be invoked
pool is the pool of assumptions (comma-separated list)
statement is the statement of logic that is to be displayed in the Formula column, without the $...$ delimiters
depends is the line (or lines) of the tableau proof upon which this line directly depends
type is the type of Rule of Idempotence: Disjunction or Conjunction, whose link will be displayed in the Notes column.