In classical logic, disjunctive syllogism[1][2] (historically known as modus tollendo ponens (MTP),[3] Latin for "mode that affirms by denying")[4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.

[5][6] An example in English: In propositional logic, disjunctive syllogism (also known as disjunction elimination and or elimination, or abbreviated ∨E),[7][8][9][10] is a valid rule of inference.

The rule makes it possible to eliminate a disjunction from a logical proof.

For a logical system that validates it, the disjunctive syllogism may be written in sequent notation as where

It may be expressed as a truth-functional tautology or theorem in the object language of propositional logic as where

are propositions expressed in some formal system.

Here is an example: Here is another example: Modus tollendo ponens can be made stronger by using exclusive disjunction instead of inclusive disjunction as a premise: Unlike modus ponens and modus ponendo tollens, with which it should not be confused, disjunctive syllogism is often not made an explicit rule or axiom of logical systems, as the above arguments can be proven with a combination of reductio ad absurdum and disjunction elimination.