Theorem rp-frege24

Description: Introducing an embedded antecedent. Alternate proof for frege24 . Closed form for a1d . (Contributed by RP, 24-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		rp-simp2-frege	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜓 ) ) )
2		ax-frege2	⊢ ( ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜓 ) ) ) → ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → 𝜓 ) → ( 𝜑 → ( 𝜒 → 𝜓 ) ) )