Theorem frege51

Description: Compare with jaod . Proposition 51 of Frege1879 p. 50. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege51	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜃 → 𝜒 ) → ( 𝜑 → ( ( ¬ 𝜓 → 𝜃 ) → 𝜒 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege50	⊢ ( ( 𝜓 → 𝜒 ) → ( ( 𝜃 → 𝜒 ) → ( ( ¬ 𝜓 → 𝜃 ) → 𝜒 ) ) )
2		frege18	⊢ ( ( ( 𝜓 → 𝜒 ) → ( ( 𝜃 → 𝜒 ) → ( ( ¬ 𝜓 → 𝜃 ) → 𝜒 ) ) ) → ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜃 → 𝜒 ) → ( 𝜑 → ( ( ¬ 𝜓 → 𝜃 ) → 𝜒 ) ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( ( 𝜃 → 𝜒 ) → ( 𝜑 → ( ( ¬ 𝜓 → 𝜃 ) → 𝜒 ) ) ) )