Rule of Conjunction

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The rule of conjunction is a valid argument in types of logic dealing with conjunctions $\land$.

This includes propositional logic and predicate logic, and in particular natural deduction.

Proof Rule

If we can conclude both $\phi$ and $\psi$, we may infer the compound statement $\phi \land \psi$.

Sequent Form

The Rule of Conjunction can be symbolised in sequent form as follows:

\(\ds p\) \(\) \(\ds \)
\(\ds q\) \(\) \(\ds \)
\(\ds \vdash \ \ \) \(\ds p \land q\) \(\) \(\ds \)


The Rule of Conjunction can be expressed in natural language as:

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

The Rule of Conjunction can also be referred to as:

  • the rule of and-introduction
  • the rule of adjunction.

Also see