Theorem frege29 41301

Description: Closed form of con3d 155. Proposition 29 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege29	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (¬ 𝜒 → ¬ 𝜓)))

Proof of Theorem frege29

Step	Hyp	Ref	Expression
1		ax-frege28 41300	. 2 ⊢ ((𝜓 → 𝜒) → (¬ 𝜒 → ¬ 𝜓))
2		frege5 41270	. 2 ⊢ (((𝜓 → 𝜒) → (¬ 𝜒 → ¬ 𝜓)) → ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (¬ 𝜒 → ¬ 𝜓))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (¬ 𝜒 → ¬ 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 41260  ax-frege2 41261  ax-frege28 41300

This theorem is referenced by:  frege30  41302