Biconditional elimination Biconditional introduction Case analysis Commutativity of conjunction Conjunction introduction Constructive dilemma Contraposition (traditional logic) Conversion (logic) De Morgan's laws Destructive dilemma Disjunction elimination Disjunction introduction Disjunctive syllogism Double negative elimination Generalization (logic) Hypothetical syllogism Law of excluded middle Law of identity Modus ponendo tollens Modus ponens Modus tollens Obversion Principle of contradiction Resolution (logic) Simplification Transposition (logic)