1. X —> ~W Premise 2. ~V —> W Premise 3.:: X Conditional Proof (CP), assumption #1 4.:: ~W 3,1 Modus Ponens (MP) 5.:: ~~V 4,2 Modus Tollens (MT) 6.:: V 5, Double Negation Elimination (DNE) 7. X —> V 3-6, CP