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 ¬ ¬ φ


Step Hyp Ref Expression
1 id ¬ φ ¬ φ
2 1 con2i φ ¬ ¬ φ