Theorem rp-4frege 43756

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 43746	. 2 ⊢ ((𝜑 → ((𝜓 → 𝜑) → 𝜒)) → (𝜑 → (𝜓 → 𝜑)))
2		rp-misc1-frege 43750	. 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))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 43744  ax-frege2 43745

This theorem is referenced by:  rp-6frege  43757