Theorem frege39

Description: Syllogism between pm2.18 and pm2.24 . Proposition 39 of Frege1879 p. 46. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege39	⊢ ( ( ¬ 𝜑 → 𝜑 ) → ( ¬ 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		frege38	⊢ ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) )
2		ax-frege2	⊢ ( ( ¬ 𝜑 → ( 𝜑 → 𝜓 ) ) → ( ( ¬ 𝜑 → 𝜑 ) → ( ¬ 𝜑 → 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( ( ¬ 𝜑 → 𝜑 ) → ( ¬ 𝜑 → 𝜓 ) )