Linked from

The 24 pages that link to Modus ponens, each with the reason it gives.

• Classical logicRelated: It is a basic rule of classical proof systems.

• Logical implicationRelated: It shows how an implication licenses a familiar deductive step.

• Material conditionalRelated: It is a basic valid inference rule for the material conditional.

• Principle of explosionRelated: Together with disjunction introduction, it derives any chosen proposition from a contradiction.

• Disjunctive syllogismRelated: Rewriting the disjunction as an implication makes the syllogism an instance of this rule.

• Peirce's lawRelated: It is a basic rule for reasoning with the implication appearing throughout the formula.

• Conjunction eliminationRelated: It can use a conjunct after elimination to satisfy an implication’s antecedent.

• Constructive dilemmaRelated: Each conditional branch of constructive dilemma applies this basic pattern to a possible antecedent.

• Deduction theoremRelated: Hilbert-system proofs commonly establish the theorem using this rule.