Theorem rp-6frege

Description: Elimination of a nested antecedent of special form. (Contributed by RP, 24-Dec-2019)

	Ref	Expression
Assertion	rp-6frege	⊢ ( 𝜑 → ( ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) → ( 𝜓 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		rp-4frege	⊢ ( ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) → ( 𝜓 → 𝜃 ) )
2		ax-frege1	⊢ ( ( ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) → ( 𝜓 → 𝜃 ) ) → ( 𝜑 → ( ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) → ( 𝜓 → 𝜃 ) ) ) )
3	1 2	ax-mp	⊢ ( 𝜑 → ( ( 𝜓 → ( ( 𝜒 → 𝜓 ) → 𝜃 ) ) → ( 𝜓 → 𝜃 ) ) )