Theorem frege24

Description: Closed form for a1d . Deduction introducing an embedded antecedent. Identical to rp-frege24 which was proved without relying on ax-frege8 . Proposition 24 of Frege1879 p. 42. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

	Ref	Expression
Assertion	frege24	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax-frege1	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) )
2		frege12	⊢ ( ( ( 𝜑 → 𝜓 ) → ( 𝜒 → ( 𝜑 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )