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Metamath Proof Explorer

Theorem notnot

Description: Double negation introduction. Converse of notnotr and one implication of notnotb . Theorem *2.12 of WhiteheadRussell p. 101. This was the sixth axiom of Frege, specifically Proposition 41 of Frege1879 p. 47. (Contributed by NM, 28-Dec-1992) (Proof shortened by Wolf Lammen, 2-Mar-2013)

		Ref	Expression
	Assertion	notnot	$⊢ φ \to \neg \neg φ$

Proof

Step	Hyp	Ref	Expression
1		id	$⊢ \neg φ \to \neg φ$
2	1	con2i	$⊢ φ \to \neg \neg φ$