©1992-2000 Colin Allen. Reproduction by any means strictly prohibited.

The text book says:
wedge-elim Given a sentence (at line m) that is a disjunction and another sentence (at line n) that is a denial of one of its disjuncts, conclude the other disjunct.
 Annotation: m, n vE
 Assumption set: The union of the assumption sets at lines m and n.
 Comment: The order of m and n in the proof is irrelevant.
 Also known as: Modus Tollendo Ponens (MTP), Disjunctive Syllogism (DS).
 
 Examples.
 (a)
 
1       (1)     P v Q                   A
 
2       (2)     ~P                      A
 
1,2     (3)     Q                       1,2 vE
 
 
 (b)
 
1       (1)     P v (Q→R)              A
 
2       (2)     ~(Q→R)                 A
 
1,2     (3)     P                       1,2 vE
 
 
 (c)
 
1       (1)     P v ~R                  A
 
2       (2)     R                       A
 
1,2     (3)     P                       1,2 vE