Theorem frege21

Description: Replace antecedent in antecedent. Proposition 21 of Frege1879 p. 40. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege21	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( ( 𝜑 → 𝜃 ) → ( ( 𝜃 → 𝜓 ) → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		frege9	⊢ ( ( 𝜑 → 𝜃 ) → ( ( 𝜃 → 𝜓 ) → ( 𝜑 → 𝜓 ) ) )
2		frege19	⊢ ( ( ( 𝜑 → 𝜃 ) → ( ( 𝜃 → 𝜓 ) → ( 𝜑 → 𝜓 ) ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( ( 𝜑 → 𝜃 ) → ( ( 𝜃 → 𝜓 ) → 𝜒 ) ) ) )
3	1 2	ax-mp	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜒 ) → ( ( 𝜑 → 𝜃 ) → ( ( 𝜃 → 𝜓 ) → 𝜒 ) ) )