Conjunction elimination

Conjunction elimination is an inference rule that derives either conjunct from a conjunction: from A ∧ B, infer A or infer B.

Conjunction introduction: An inference rule that derives A ∧ B from premises A and B. It reverses elimination by combining two established statements into their conjunction.
Proposition: A declarative statement that can be assigned a truth value. The variables A and B stand for propositions to which the rule applies.
Modus ponens: An inference rule that derives B from A and A → B. It can use a conjunct after elimination to satisfy an implication’s antecedent.
Disjunction elimination: An inference rule that derives a conclusion from a disjunction by proving it from each disjunct. Unlike conjunction elimination, it requires reasoning through separate cases.
Natural deduction: A proof system that represents reasoning through introduction and elimination rules for logical connectives. Conjunction elimination is one of its basic connective rules.
Logical connective: An expression that combines or modifies propositions to form more complex propositions. Conjunction elimination operates on a formula built with a connective.
Conditional proof: A proof method that assumes an antecedent temporarily and derives its consequent. A conjunction premise can supply the assumption needed within a conditional proof.
Conjunction fallacy: The mistaken judgment that a conjunction is more probable than one of its individual components. The fallacy violates the probability relation that makes conjunction elimination intuitively plausible.
Sequent calculus: A proof system that represents derivations as transformations between structured collections of formulas. Its left rule for conjunction captures the same reasoning in a different proof format.
Premise: A statement assumed or established as support for a conclusion in an argument or proof. The conjunction is the premise from which the rule licenses an inference.

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