# Rule of Idempotence

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## 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.

## Sources

- 1973: Irving M. Copi:
*Symbolic Logic*(4th ed.) ... (previous) ... (next): $3.2$: The Rule of Replacement