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	$$⊢\phi \to \neg \neg \phi$$

Proof

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