Theorem frege14 41431

Description: Closed form of a deduction based on com3r 87. Proposition 14 of [Frege1879] p. 37. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege14	⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏)))))

Proof of Theorem frege14

Step	Hyp	Ref	Expression
1		frege13 41430	. 2 ⊢ ((𝜓 → (𝜒 → (𝜃 → 𝜏))) → (𝜃 → (𝜓 → (𝜒 → 𝜏))))
2		frege5 41408	. 2 ⊢ (((𝜓 → (𝜒 → (𝜃 → 𝜏))) → (𝜃 → (𝜓 → (𝜒 → 𝜏)))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏))))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜃 → (𝜓 → (𝜒 → 𝜏)))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 41398  ax-frege2 41399  ax-frege8 41417

This theorem is referenced by:  frege15  41434