Rule of Conjunction

Proof Rule
The rule of conjunction is a valid deduction sequent in propositional logic: If we can conclude both $p$ and $q$, we may infer the compound statement $p \land q$.

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

Explanation
This means: if we can show that two statements are true, then we may build a compound statement expressing this fact, and be certain that this is also true.

Thus a conjunction is added to a sequent.

Also known as
This is sometimes known as:


 * the rule of and-introduction;
 * the rule of adjunction.

Also see

 * Rule of Simplification

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



or:

where:
 * is the number of the line on the tableau proof where the Rule of Conjunction 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 first of the two lines of the tableau proof upon which this line directly depends
 * is the second of the two lines of the tableau proof upon which this line directly depends
 * is the (optional) comment that is to be displayed in the Notes column.