Theorem rp-simp2-frege 44736

Description: Simplification of triple conjunction. Compare with simp2 1155. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
rp-simp2-frege	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))

Proof of Theorem rp-simp2-frege

Step	Hyp	Ref	Expression
1		ax-frege1 44734	. 2 ⊢ (𝜓 → (𝜒 → 𝜓))
2		ax-frege1 44734	. 2 ⊢ ((𝜓 → (𝜒 → 𝜓)) → (𝜑 → (𝜓 → (𝜒 → 𝜓))))
3	1, 2	ax-mp 5	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44734

This theorem is used by:  rp-simp2  44737  rp-frege24  44741  rp-4frege  44746