Theorem frege44

Description: Similar to a commuted pm2.62 . Proposition 44 of Frege1879 p. 47. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege44	⊢ ( ( ¬ 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜑 ) → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		frege43	⊢ ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 )
2		frege21	⊢ ( ( ( ¬ 𝜑 → 𝜑 ) → 𝜑 ) → ( ( ¬ 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜑 ) → 𝜑 ) ) )
3	1 2	ax-mp	⊢ ( ( ¬ 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜑 ) → 𝜑 ) )