Theorem rp-frege4g 44565

Description: Deduction related to distribution. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-frege4g	⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → ((𝜓 → 𝜒) → (𝜓 → 𝜃))))

Proof of Theorem rp-frege4g

Step	Hyp	Ref	Expression
1		rp-frege3g 44561	. 2 ⊢ (𝜑 → ((𝜓 → (𝜒 → 𝜃)) → ((𝜓 → 𝜒) → (𝜓 → 𝜃))))
2		ax-frege2 44558	. 2 ⊢ ((𝜑 → ((𝜓 → (𝜒 → 𝜃)) → ((𝜓 → 𝜒) → (𝜓 → 𝜃)))) → ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → ((𝜓 → 𝜒) → (𝜓 → 𝜃)))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → ((𝜓 → 𝜒) → (𝜓 → 𝜃))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44557  ax-frege2 44558

This theorem is used by: (None)