Conjunction introduction

Conjunction introduction is a rule of inference that derives P ∧ Q from established propositions P and Q. It is valid in classical and intuitionistic logic.

Natural deduction: A proof system that represents reasoning through introduction and elimination rules for logical operators. Conjunction introduction is one of natural deduction’s standard introduction rules.
Proposition: A declarative statement that can be assigned a truth value. P and Q are propositions that the rule combines.
Proof theory: The study of formal proofs, their structure, and the systems that generate them. It analyzes conjunction introduction as a component of proof systems.
Disjunction introduction: A rule of inference that derives a disjunction when either one of its disjuncts is established. Unlike conjunction introduction, it needs only one established proposition.
Sequent calculus: A formal proof system that derives sequents using structured inference rules. Its right-conjunction rule expresses the same two-premise pattern in a different proof framework.
Logical connective: An expression that combines or modifies propositions to form compound propositions. Conjunction introduction applies specifically to the connective ∧.
Propositional logic: A logic whose basic units are propositions combined by logical connectives. The rule operates directly on propositions in this logical framework.
Implication introduction: A rule of inference that derives an implication by showing its consequent from an assumed antecedent. It discharges an assumption, whereas conjunction introduction combines two established claims.
Conjunction: A logical connective that forms a compound proposition true exactly when both component propositions are true. The rule introduces this connective into a proof.
Logical consequence: A relation in which a conclusion must be true whenever its premises are true. The rule preserves this relation from P and Q to P ∧ Q.

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