Rules of inference

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Modus ponens Modus tollens Modus ponendo tollens Modus non excipiens Hypothetical syllogism Disjunctive syllogism Constructive dilemma Destructive dilemma Conjunction introduction Conjunction elimination Disjunction introduction Disjunction elimination Biconditional introduction Biconditional elimination Negation introduction Double negation elimination Universal instantiation Universal generalization Existential generalization Existential instantiation Proof by cases Reductio ad absurdum Resolution logic First order resolution Superposition calculus Rule of replacement Transposition logic Exportation logic Absorption logic Simplification logic Commutativity of conjunction Idempotency of entailment Monotonicity of entailment Material implication rule of inference De morgans laws Peirces law Principle of explosion Ex contradictione quodlibet Immediate inference Contraposition traditional logic Conversion logic Obversion Subalternation Generalization logic Substitution instance Tautology rule of inference

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