Modus ponens
if X implies Y, and X is true, then Y is true
In propositional logic, modus ponens (; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q. P is true. Therefore, Q must also be true."
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens.
The history of modus ponens goes back to antiquity. The first to explicitly describe the argument form modus ponens was Theophrastus. It, along with modus tollens, is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal.
Explanation
The form of a modus ponens argument is a mixed hypothetical syllogism, with two premises and a conclusion:
If P, then Q.
P.
Therefore, Q.
The first (major) premise is a conditional ("if–then") claim, namely that P implies Q. The second (minor) premise is an assertion that P, the antecedent of the conditional claim, is the case. From these two premises it can be logically concluded that Q, the consequent of the conditional claim, must be the case as well.
Begin with the source’s own compact description: “Modus ponens” is if X implies Y, and X is true, then Y is true. The dossier treats that line as a proposition to test through Modus, ponens and implies, not as a finished interpretation.
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The phrase “if X implies Y, and X is true, then Y is true” supplies a clear boundary for inquiry. It also exposes the unanswered questions: who defined that boundary, when it became stable and which sources sit outside it.
Named sources, stable identifiers and responsible institutions provide the strongest route from overview to verifiable evidence. The source revision retrieved here is dated Sep 19, 2026. The linked authority identifier is Q655742. None of the 0 selected statements returned an explicit reference.
Overview language is designed for orientation and should not be treated as a substitute for the evidence cited beneath it. The lead is largely declarative, so disagreement and counter-evidence require a deliberate search beyond the opening account. Authority statements aid reconciliation but still require their own references, qualifiers and ranks to be checked.
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This entry incorporates text from “Modus ponens” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.