Theorem rp-8frege

Description: Eliminate antecedent when it is implied by previous antecedent. (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	rp-8frege	⊢ ( ( 𝜑 → ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) ) → ( 𝜑 → ( 𝜓 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		rp-6frege	⊢ ( 𝜑 → ( ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) → ( 𝜓 → 𝜃 ) ) )
2		ax-frege2	⊢ ( ( 𝜑 → ( ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) → ( 𝜓 → 𝜃 ) ) ) → ( ( 𝜑 → ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) ) → ( 𝜑 → ( 𝜓 → 𝜃 ) ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) ) → ( 𝜑 → ( 𝜓 → 𝜃 ) ) )