Theorem frege42 44845

Description: Not not id 23. 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 44810	. 2 ⊢ (𝜑 → 𝜑)
2		ax-frege41 44844	. 2 ⊢ ((𝜑 → 𝜑) → ¬ ¬ (𝜑 → 𝜑))
3	1, 2	ax-mp 5	1 ⊢ ¬ ¬ (𝜑 → 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44789  ax-frege8 44808  ax-frege41 44844

This theorem is used by:  frege43  44846