Theorem rp-4frege 44556

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

Assertion

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

Proof of Theorem rp-4frege

Step	Hyp	Ref	Expression
1		rp-simp2-frege 44546	. 2 ⊢ ((𝜑 → ((𝜓 → 𝜑) → 𝜒)) → (𝜑 → (𝜓 → 𝜑)))
2		rp-misc1-frege 44550	. 2 ⊢ (((𝜑 → ((𝜓 → 𝜑) → 𝜒)) → (𝜑 → (𝜓 → 𝜑))) → ((𝜑 → ((𝜓 → 𝜑) → 𝜒)) → (𝜑 → 𝜒)))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → ((𝜓 → 𝜑) → 𝜒)) → (𝜑 → 𝜒))

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-6frege  44557