Theorem frege42 37160

Description: Not not id 22. Proposition 42 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege42	⊢ ¬ ¬ (𝜑 → 𝜑)

Proof of Theorem frege42

Step	Hyp	Ref	Expression
1		frege27 37125	. 2 ⊢ (𝜑 → 𝜑)
2		ax-frege41 37159	. 2 ⊢ ((𝜑 → 𝜑) → ¬ ¬ (𝜑 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ¬ ¬ (𝜑 → 𝜑)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 37104  ax-frege8 37123  ax-frege41 37159

This theorem is referenced by:  frege43  37161