Theorem frege29

Description: Closed form of con3d . Proposition 29 of Frege1879 p. 43. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege29	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege28	⊢ ( ( 𝜓 → 𝜒 ) → ( ¬ 𝜒 → ¬ 𝜓 ) )
2		frege5	⊢ ( ( ( 𝜓 → 𝜒 ) → ( ¬ 𝜒 → ¬ 𝜓 ) ) → ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( ¬ 𝜒 → ¬ 𝜓 ) ) )