Theorem frege25 44571

Description: Closed form for a1dd 51. Proposition 25 of [Frege1879] p. 42. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege25

Step	Hyp	Ref	Expression
1		frege24 44569	. 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  ax-frege8 44563

This theorem is used by:  frege111  44728