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Metamath Proof Explorer

Theorem notnotb

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

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

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