Rule of Simplification

Proof Rule
The rule of simplification is a valid deduction sequent in propositional logic:

This is two axioms in one:
 * $(1): \quad$ If we can conclude $p \land q$, then we may infer $p$.
 * $(2): \quad$ If we can conclude $p \land q$, then we may infer $q$.

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

Explanation
Note that there are two axioms here in one. The first of the two tells us that, given a conjunction, we may infer the first of the conjuncts, while the second says that, given a conjunction, we may infer the second of the conjuncts.

At this stage, such attention to detail is important.

Also known as
This is sometimes known as the rule of and-elimination.

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 assumption 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.