Axioms in logic

[Quantifiers](https://en.wikipedia.org/wiki/Quantifier_(logic)) [Predicate](https://en.wikipedia.org/wiki/Predicate_(mathematical_logic)) Connective [Tautology](https://en.wikipedia.org/wiki/Tautology_(logic)) Truth tables Truth function Truth value Monotonicity of entailment Idempotency of entailment Logicism Problem of multiple generality Associativity Distribution Well-formed formula

Commutativity of conjunction Excluded middle Bivalence Noncontradiction

De Morgan's laws

[Material implication](https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference)) modus ponens modus tollens modus ponendo tollens [Transposition](https://en.wikipedia.org/wiki/Transposition_(logic))

Biconditional introduction Biconditional elimination

Constructive dilemma Destructive dilemma

Disjunctive syllogism Hypothetical syllogism

[Absorption](https://en.wikipedia.org/wiki/Absorption_(logic))

Negation introduction Double negation introduction

Universal generalization Existential generalization Universal instantiation Existential instantiation

• Conjunction introduction

• Disjunction introduction

• Conjunction elimination

• Disjunction elimination