Theorem rp-8frege 40170

Description: Eliminate antecedent when it is implied by previous antecedent. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-8frege	⊢ ((𝜑 → (𝜓 → ((𝜒 → 𝜓) → 𝜃))) → (𝜑 → (𝜓 → 𝜃)))

Proof of Theorem rp-8frege

Step	Hyp	Ref	Expression
1		rp-6frege 40169	. 2 ⊢ (𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃)))
2		ax-frege2 40157	. 2 ⊢ ((𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃))) → ((𝜑 → (𝜓 → ((𝜒 → 𝜓) → 𝜃))) → (𝜑 → (𝜓 → 𝜃))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → ((𝜒 → 𝜓) → 𝜃))) → (𝜑 → (𝜓 → 𝜃)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 40156  ax-frege2 40157

This theorem is referenced by:  axfrege8  40173