Theorem frege35 45028

Description: Commuted, closed form of con1d 146. Proposition 35 of [Frege1879] p. 45. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege35	⊢ ((𝜑 → (¬ 𝜓 → 𝜒)) → (¬ 𝜒 → (𝜑 → 𝜓)))

Proof of Theorem frege35

Step	Hyp	Ref	Expression
1		frege34 45027	. 2 ⊢ ((𝜑 → (¬ 𝜓 → 𝜒)) → (𝜑 → (¬ 𝜒 → 𝜓)))
2		frege12 45003	. 2 ⊢ (((𝜑 → (¬ 𝜓 → 𝜒)) → (𝜑 → (¬ 𝜒 → 𝜓))) → ((𝜑 → (¬ 𝜓 → 𝜒)) → (¬ 𝜒 → (𝜑 → 𝜓))))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 → (¬ 𝜓 → 𝜒)) → (¬ 𝜒 → (𝜑 → 𝜓)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-frege1 44980  ax-frege2 44981  ax-frege8 44999  ax-frege28 45020  ax-frege31 45024

This theorem is used by:  frege40  45033