Theorem notnotr

Double negation elimination. Converse of notnot and one implication of notnotb. Theorem *2.14 of [WhiteheadRussell] p. 102. This was the fifth axiom of Frege, specifically Proposition 31 of [Frege1879] p. 44. In classical logic (our logic) this is always true. In intuitionistic logic this is not always true, and formulas for which it is true are called "stable". (Contributed by NM, 29-Dec-1992.) (Proof shortened by David Harvey, 5-Sep-1999.) (Proof shortened by Josh Purinton, 29-Dec-2000.)

Conclusion
\( \vdash \neg \neg \varphi \rightarrow \varphi \)
Proof
pm2.18
\( \vdash (\neg \varphi \rightarrow \varphi) \rightarrow \varphi \)
jarli _