Theorem frege12 43802

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 43798	. 2 ⊢ ((𝜓 → (𝜒 → 𝜃)) → (𝜒 → (𝜓 → 𝜃)))
2		frege5 43789	. 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 43779  ax-frege2 43780  ax-frege8 43798

This theorem is referenced by:  frege24  43804  frege16  43805  frege13  43811  frege15  43815  frege35  43827  frege49  43842  frege60a  43867  frege60b  43894  frege60c  43912  frege85  43937  frege127  43979