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