Linked from

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

• Deductive reasoningBroader topic: This basic rule shows how a conclusion can follow necessarily from premises.

• Propositional logicBroader topic: This basic rule derives conclusions from conditionals in propositional proofs.

• Rule of inferenceBroader topic: It is the standard example of a rule applied to two premises.

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

• Formal proofBroader topic: This basic rule illustrates how a proof step applies stated premises.

• SoundnessBroader topic: Its validity illustrates how a single truth-preserving rule supports sound derivations.

• Stoic logicBroader topic: It is the first of the traditional Stoic indemonstrable argument forms.

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

• Modus tollensCompared with: It uses the same conditional structure but affirms P rather than denying Q.

• SyllogismCompared with: This propositional rule illustrates valid deduction without a three-term categorical structure.

• Logical formBroader topic: It is a standard valid form used across subjects and ordinary reasoning.

• Logical validityBroader topic: This canonical valid form preserves truth from premises to conclusion.

• 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.

• Affirming the consequentCompared with: It preserves the conditional’s direction, unlike affirming the consequent.

• Disjunction eliminationCompared with: It applies a conditional directly, rather than splitting a disjunctive premise into cases.

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

• Conjunction introductionCompared with: It uses one proposition to apply a conditional, rather than joining propositions with ∧.

• Formal fallacyCompared with: It is the valid conditional pattern commonly confused with affirming the consequent.

• 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.

• Modus ponendo tollensCompared with: It uses a conditional rather than mutually exclusive alternatives.