Theorem frege16 41313

Description: A closed form of com34 91. Proposition 16 of [Frege1879] p. 38. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege16	⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏)))))

Proof of Theorem frege16

Step	Hyp	Ref	Expression
1		frege12 41310	. 2 ⊢ ((𝜓 → (𝜒 → (𝜃 → 𝜏))) → (𝜓 → (𝜃 → (𝜒 → 𝜏))))
2		frege5 41297	. 2 ⊢ (((𝜓 → (𝜒 → (𝜃 → 𝜏))) → (𝜓 → (𝜃 → (𝜒 → 𝜏)))) → ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏))))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) → (𝜑 → (𝜓 → (𝜃 → (𝜒 → 𝜏)))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 41287  ax-frege2 41288  ax-frege8 41306

This theorem is referenced by:  frege18  41315  frege22  41316  frege17  41318