Theorem frege40

Description: Anything implies pm2.18 . Proposition 40 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege40	⊢ ( ¬ 𝜑 → ( ( ¬ 𝜓 → 𝜓 ) → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		frege39	⊢ ( ( ¬ 𝜓 → 𝜓 ) → ( ¬ 𝜓 → 𝜑 ) )
2		frege35	⊢ ( ( ( ¬ 𝜓 → 𝜓 ) → ( ¬ 𝜓 → 𝜑 ) ) → ( ¬ 𝜑 → ( ( ¬ 𝜓 → 𝜓 ) → 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( ¬ 𝜑 → ( ( ¬ 𝜓 → 𝜓 ) → 𝜓 ) )