A rule of inference that permits forming the conjunction A ∧ B when both A and B have been established separately.

Principle

Two independently established formulas can be combined into a single formula asserting both hold; conjunction records joint truth.

Demonstration

Given a proof of A and a proof of B, apply conjunction introduction to infer A ∧ B. Example: from 'It rains' and 'The ground is wet' infer 'It rains ∧ The ground is wet.'

Misapplication

Using the rule with only one proven conjunct (attempting to infer A ∧ B from A alone without separately establishing B), or treating conjunction introduction as reversible without applying conjunction elimination and re-proving components.

Consequence

Enables construction of compound statements and packaging of separate results into a single hypothesis usable by later rules; it is fundamental for building complex derivations from simpler facts.

Reversal

Contrasts with conjunction elimination: instead of breaking a conjunction into parts (A ∧ B ⇒ A), introduction composes parts into a whole. Reversing incorrectly would claim a conjunction suffices to produce unrelated new facts.

Boundary

Valid in classical and intuitionistic logics and most deductive systems that accept conjunction; in substructural logics restrictions on structural rules may affect how premises are combined. It presumes separate justifications for each conjunct.

Semantic Tension

Tension exists between the syntactic convenience of freely combining proven formulas and concerns about dependency or resource-sensitivity in logics where hypotheses cannot be arbitrarily duplicated or combined.

Synthesis

Conjunction introduction is the syntactic operation that assembles independently established propositions into a single proposition asserting their joint truth, serving as the constructive building block for composite facts.