Theorem frege20 38122

Description: A closed form of syl8 76. Proposition 20 of [Frege1879] p. 40. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege20	⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → ((𝜃 → 𝜏) → (𝜑 → (𝜓 → (𝜒 → 𝜏)))))

Proof of Theorem frege20

Step	Hyp	Ref	Expression
1		frege19 38118	. 2 ⊢ ((𝜓 → (𝜒 → 𝜃)) → ((𝜃 → 𝜏) → (𝜓 → (𝜒 → 𝜏))))
2		frege18 38112	. 2 ⊢ (((𝜓 → (𝜒 → 𝜃)) → ((𝜃 → 𝜏) → (𝜓 → (𝜒 → 𝜏)))) → ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → ((𝜃 → 𝜏) → (𝜑 → (𝜓 → (𝜒 → 𝜏))))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → ((𝜃 → 𝜏) → (𝜑 → (𝜓 → (𝜒 → 𝜏)))))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 38084  ax-frege2 38085  ax-frege8 38103

This theorem is referenced by:  frege121  38278  frege125  38282