Description: Modus tollendo ponens (inclusive-or version), aka disjunctive syllogism.
This is similar to mtpxor , one of the five original "indemonstrables"
in Stoic logic. However, in Stoic logic this rule used exclusive-or,
while the name modus tollendo ponens often refers to a variant of the
rule that uses inclusive-or instead. The rule says, "if ph is not
true, and ph or ps (or both) are true, then ps must be
true". An alternate phrasing is: "once you eliminate the impossible,
whatever remains, no matter how improbable, must be the truth". --
Sherlock Holmes (Sir Arthur Conan Doyle, 1890: The Sign of the Four,
ch. 6). (Contributed by David A. Wheeler, 3-Jul-2016)(Proof
shortened by Wolf Lammen, 11-Nov-2017)