Rule of Explosion

Proof Rule
The Rule of Explosion is a valid deduction sequent in propositional logic.

Proof Rule
If a contradiction can be concluded, it is possible to infer any statement.

It can be written:
 * $\displaystyle{\bot \over p} \bot_e$

Variants
The following can be used as variants of this theorem:

Also see

 * False Statement implies Every Statement

Technical Note
When invoking the Rule of Explosion in a tableau proof, use the BottomElimination template:



or:

where:
 * is the number of the line on the tableau proof where Rule of Explosion is to be invoked
 * is the pool of assumptions (comma-separated list)
 * is the statement of logic that is to be displayed in the Formula column, without the  delimiters
 * is the line of the tableau proof upon which this line directly depends, the one with $\bot$ on it
 * is the (optional) comment that is to be displayed in the Notes column.