Constructive dilemma
Constructive dilemma is a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either P or R is true, then either Q or S has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be too. Constructive dilemma is the disjunctive version of modus ponens, whereas,
destructive dilemma is the disjunctive version of modus tollens. The constructive dilemma rule can be stated:

where the rule is that whenever instances of "", "", and "" appear on lines of a proof, "" can be placed on a subsequent line. Formal notation 
The constructive dilemma rule may be written in sequent notation:

 

where  is a metalogical symbol meaning that  is a syntactic consequence of , , and  in some logical system;

and expressed as a truth-functional tautology or theorem of propositional logic:

where , ,  and  are propositions expressed in some formal system. Natural language example 

If I win a million dollars, I will donate it to an orphanage. If my friend wins a million dollars, he will donate it to a wildlife fund. Either I win a million dollars or my friend wins a million dollars. Therefore, either an orphanage will get a million dollars, or a wildlife fund will get a million dollars. The dilemma derives its name because of the transfer of disjunctive operator. References

Rules of inference
Dilemmas
Theorems in propositional logic