Theorem rp-frege4g

Description: Deduction related to distribution. (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	rp-frege4g	⊢ ( ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) → ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		rp-frege3g	⊢ ( 𝜑 → ( ( 𝜓 → ( 𝜒 → 𝜃 ) ) → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) )
2		ax-frege2	⊢ ( ( 𝜑 → ( ( 𝜓 → ( 𝜒 → 𝜃 ) ) → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) ) → ( ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) → ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) ) → ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → 𝜃 ) ) ) )