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A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules.

Here is the original question:https://philosophy.stackexchange.com/a/54040/42555

I am not familiar with "DS" as a method

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  • Which question was that? Click on the "share" link by that question and copy it. Then paste that link in your question. This may help to provide context for the steps that are confusing. Oct 7, 2019 at 13:44
  • "intro and elim rules, as well as contradiction rules"... There are no other rules for propositional connectives. Oct 7, 2019 at 13:57
  • The DS is disjunctive syllogism: en.wikipedia.org/wiki/Disjunctive_syllogism One could use disjunction elimination instead. Consider each disjunct from ~P v Q in line 1 as a separate subproof. First consider ~P. That contradicts line 2 which leads to a contradiction. From that contradiction derive Q using contradiction elimination. Then consider Q. That is what you want so there is nothing to do. In both cases you have derived Q and so you can eliminate the disjunction and derive Q. From there you can derive P -> Q. Oct 7, 2019 at 19:55
  • You are right : DS is not necessary. There is an answer to the original question that uses only intro- and elim- rules. Oct 9, 2019 at 8:00

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