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Theorem frege30 37946
Description: Commuted, closed form of con3d 148. Proposition 30 of [Frege1879] p. 44. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege30 ((𝜑 → (𝜓𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))

Proof of Theorem frege30
StepHypRef Expression
1 frege29 37945 . 2 ((𝜓 → (𝜑𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))
2 frege10 37934 . 2 (((𝜓 → (𝜑𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))) → ((𝜑 → (𝜓𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓𝜒)) → (𝜓 → (¬ 𝜒 → ¬ 𝜑)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 37904  ax-frege2 37905  ax-frege8 37923  ax-frege28 37944
This theorem is referenced by:  frege59a  37991  frege59b  38018  frege59c  38036
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