Theorem rp-frege24 42548

Description: Introducing an embedded antecedent. Alternate proof for frege24 42566. Closed form for a1d 25. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-frege24	⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓)))

Proof of Theorem rp-frege24

Step	Hyp	Ref	Expression
1		rp-simp2-frege 42543	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜓)))
2		ax-frege2 42542	. 2 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜓))) → ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜒 → 𝜓)))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 42541  ax-frege2 42542

This theorem is referenced by:  rp-7frege  42552  rp-frege25  42556