Theorem frege14 44822

Description: Closed form of a deduction based on com3r 88. 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 44821	. 2 ⊢ ((𝜓 → (𝜒 → (𝜃 → 𝜏))) → (𝜃 → (𝜓 → (𝜒 → 𝜏))))
2		frege5 44799	. 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)))))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44789  ax-frege2 44790  ax-frege8 44808

This theorem is used by:  frege15  44825