Wikiproofs:Scattered propositional logic theorems

This is a list of propositional logic theorems which are proved outside Category:Classical propositional logic. There are a number of ways of reacting to this situation:


 * 1) This theorem is only used one place (and perhaps is unlikely to be needed anywhere else), but it does make this particular proof more clear, so don't worry about it.
 * 2) This theorem is unnecessary; it would be simpler to just avoid it (for example, metamath's set.mm has a theorem to apply modus ponens twice, but at least so far in wikiproofs our decision has been that   expresses this idea just as clearly).
 * 3) This theorem made it easier to translate a proof from another source, but ultimately it will be clearer to rearrange the proof using our usual idioms.
 * 4) This is really a fundamental theorem which belongs alongside the other core theorems of propositional logic in Interface:Principia Mathematica propositional logic theorems. Whether the theorem is in Principia is perhaps the largest criterion for whether it is fundamental. Others are whether it expresses a relationship between the various connectives or a statement which is not easily proved from other theorems.
 * 5) This is a convenience theorem which probably should be in Interface:Classical propositional calculus but is an easy consequence of the fundamental theorems and is therefore more naturally proved in Convenience theorems of propositional logic.

The list
From First-order logic:


 * principia*2.21