Theorem rp-frege25 44559

Description: Closed form for a1dd 51. Alternate route to Proposition 25 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.)

Assertion

Ref	Expression
rp-frege25	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜃 → 𝜒))))

Proof of Theorem rp-frege25

Step	Hyp	Ref	Expression
1		rp-frege24 44551	. 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → (𝜃 → 𝜒)))
2		frege5 44554	. 2 ⊢ (((𝜓 → 𝜒) → (𝜓 → (𝜃 → 𝜒))) → ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜃 → 𝜒)))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜃 → 𝜒))))

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: (None)