¬ ¬ A ∴ AAlso:
¬ ¬ ¬ A ∴ ¬ AThe rule of double negative introduction states the converse, that double negatives can be added without changing the meaning of a proposition.
This rule is true in classical logic, but in intuitionistic logic, the statement, It's not the case that it's not raining. is weaker than It's raining.. As a slightly clearer example, It's not unreasonable is slightly less direct than It's reasonable.
In naive set theory also we have the negation operation of the complement which obeys this property: a set A and a set A'' (where A' represents the complement of A) are the same.