Theorem rp-4frege

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

	Ref	Expression
Assertion	rp-4frege	⊢ ( ( 𝜑 → ( ( 𝜓 → 𝜑 ) → 𝜒 ) ) → ( 𝜑 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		rp-simp2-frege	⊢ ( ( 𝜑 → ( ( 𝜓 → 𝜑 ) → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → 𝜑 ) ) )
2		rp-misc1-frege	⊢ ( ( ( 𝜑 → ( ( 𝜓 → 𝜑 ) → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → 𝜑 ) ) ) → ( ( 𝜑 → ( ( 𝜓 → 𝜑 ) → 𝜒 ) ) → ( 𝜑 → 𝜒 ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜑 → ( ( 𝜓 → 𝜑 ) → 𝜒 ) ) → ( 𝜑 → 𝜒 ) )