Theorem rp-6frege 44557

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

Assertion

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

Proof of Theorem rp-6frege

Step	Hyp	Ref	Expression
1		rp-4frege 44556	. 2 ⊢ ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃))
2		ax-frege1 44544	. 2 ⊢ (((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃)) → (𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃))))
3	1, 2	ax-mp 5	1 ⊢ (𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44544  ax-frege2 44545

This theorem is used by:  rp-8frege  44558