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Theorem frege29 36944
Description: Closed form of con3d 146. Proposition 29 of [Frege1879] p. 43. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege29 ((𝜑 → (𝜓𝜒)) → (𝜑 → (¬ 𝜒 → ¬ 𝜓)))

Proof of Theorem frege29
StepHypRef Expression
1 ax-frege28 36943 . 2 ((𝜓𝜒) → (¬ 𝜒 → ¬ 𝜓))
2 frege5 36913 . 2 (((𝜓𝜒) → (¬ 𝜒 → ¬ 𝜓)) → ((𝜑 → (𝜓𝜒)) → (𝜑 → (¬ 𝜒 → ¬ 𝜓))))
31, 2ax-mp 5 1 ((𝜑 → (𝜓𝜒)) → (𝜑 → (¬ 𝜒 → ¬ 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36903  ax-frege2 36904  ax-frege28 36943
This theorem is referenced by:  frege30  36945
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