Theorem frege30 41329

Description: Commuted, closed form of con3d 152. Proposition 30 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege30	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))

Proof of Theorem frege30

Step	Hyp	Ref	Expression
1		frege29 41328	. 2 ⊢ ((𝜓 → (𝜑 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))
2		frege10 41317	. 2 ⊢ (((𝜓 → (𝜑 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))) → ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-frege1 41287  ax-frege2 41288  ax-frege8 41306  ax-frege28 41327

This theorem is referenced by:  frege59a  41374  frege59b  41401  frege59c  41419