Theorem notnotb

Description: Double negation. Theorem *4.13 of WhiteheadRussell p. 117. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Assertion	notnotb	$$⊢\phi \leftrightarrow \neg \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		notnot	$$⊢\phi \to \neg \neg \phi$$
2		notnotr	$$⊢\neg \neg \phi \to \phi$$
3	1 2	impbii	$$⊢\phi \leftrightarrow \neg \neg \phi$$