Rule of Simplification/Proof Rule

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

As a proof rule it is expressed in either of the two forms:
 * $(1): \quad$ If we can conclude $\phi \land \psi$, then we may infer $\phi$.
 * $(2): \quad$ If we can conclude $\phi \land \psi$, then we may infer $\psi$.

It can be written:
 * $\displaystyle {\phi \land \psi \over \phi} \land_{e_1} \qquad \qquad {\phi \land \psi \over \psi} \land_{e_2}$

Also see

 * Rule of Conjunction

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



or:

where:
 * is the number of the line on the tableau proof where the Rule of Simplification 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
 * should hold 1 for Simplification_1, and 2 for Simplification_2
 * is the (optional) comment that is to be displayed in the Notes column.