@leafy,
leafy;98632 wrote:Doesn't that rely on Disjunctive Syllogism or Reductio Ad Absurdum?
No it does not. Logical implication is defined in a way such that it directly follows from the definition. With the possible worlds' approach it is defined something like this:
[INDENT]P implies Q iff there is no possible world where it is not the case that Q and it is the case that P.
[/INDENT]Obviously if there is no possible world where P is the case, then there is no possible world where P is the case and Q is not the case.