Theorem frege12 38107

Description: A closed form of com23 86. Proposition 12 of [Frege1879] p. 37. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege12	⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → (𝜒 → (𝜓 → 𝜃))))

Proof of Theorem frege12

Step	Hyp	Ref	Expression
1		ax-frege8 38103	. 2 ⊢ ((𝜓 → (𝜒 → 𝜃)) → (𝜒 → (𝜓 → 𝜃)))
2		frege5 38094	. 2 ⊢ (((𝜓 → (𝜒 → 𝜃)) → (𝜒 → (𝜓 → 𝜃))) → ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → (𝜒 → (𝜓 → 𝜃)))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → (𝜒 → 𝜃))) → (𝜑 → (𝜒 → (𝜓 → 𝜃))))

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:  frege24  38109  frege16  38110  frege13  38116  frege15  38120  frege35  38132  frege49  38147  frege60a  38172  frege60b  38199  frege60c  38217  frege85  38242  frege127  38284