Destructive dilemma[1][2] is the name of a valid rule of inference of propositional logic.

In sum, if two conditionals are true, but one of their consequents is false, then one of their antecedents has to be false.

Destructive dilemma is the disjunctive version of modus tollens.

The disjunctive version of modus ponens is the constructive dilemma.

The destructive dilemma rule may be written in sequent notation: where

is a metalogical symbol meaning that

in some logical system; and expressed as a truth-functional tautology or theorem of propositional logic: where

are propositions expressed in some formal system.

The validity of this argument structure can be shown by using both conditional proof (CP) and reductio ad absurdum (RAA) in the following way: