Metamath Proof Explorer


Axiom ax-frege41

Description: The affirmation of ph denies the denial of ph . Identical to notnot . Axiom 41 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (New usage is discouraged.)

Ref Expression
Assertion ax-frege41 ( 𝜑 → ¬ ¬ 𝜑 )

Detailed syntax breakdown

Step Hyp Ref Expression
0 wph 𝜑
1 0 wn ¬ 𝜑
2 1 wn ¬ ¬ 𝜑
3 0 2 wi ( 𝜑 → ¬ ¬ 𝜑 )