Theorem rp-8frege 44558

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 44557	. 2 ⊢ (𝜑 → ((𝜓 → ((𝜒 → 𝜓) → 𝜃)) → (𝜓 → 𝜃)))
2		ax-frege2 44545	. 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)))

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:  axfrege8  44561