Theorem frege12 40179

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 40175	. 2 ⊢ ((𝜓 → (𝜒 → 𝜃)) → (𝜒 → (𝜓 → 𝜃)))
2		frege5 40166	. 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 40156  ax-frege2 40157  ax-frege8 40175

This theorem is referenced by:  frege24  40181  frege16  40182  frege13  40188  frege15  40192  frege35  40204  frege49  40219  frege60a  40244  frege60b  40271  frege60c  40289  frege85  40314  frege127  40356