List of rules of inference

A list of commonly used rules of inference.

• Reductio ad absurdum

Known Conditional Transformation Rules

• Modus ponens
• Modus tollens
• Conjunction
• Disjunction
• Simplification
• Addition
• Repetition
• Disjunctive syllogism
• Hypothetical syllogism
• Constructive dilemma
• Destructive dilemma

Known Biconditional Transformation Rules

• Double negative elimination
• Implication
• Contraposition
• Exportation
• Distribution
• De Morgan's Laws
• Commutation
• Association
• Tautology
• Equivalence

Hypothetical Transformation Rules

• Conditional proof
• Indirect proof