Rule of Conjunction/Proof Rule

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

As a proof rule it is expressed in the form:
 * If we can conclude both $\phi$ and $\psi$, we may infer the compound statement $\phi \land \psi$.

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

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.