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Theorem frege35 40470
Description: Commuted, closed form of con1d 147. Proposition 35 of [Frege1879] p. 45. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege35 ((𝜑 → (¬ 𝜓𝜒)) → (¬ 𝜒 → (𝜑𝜓)))

Proof of Theorem frege35
StepHypRef Expression
1 frege34 40469 . 2 ((𝜑 → (¬ 𝜓𝜒)) → (𝜑 → (¬ 𝜒𝜓)))
2 frege12 40445 . 2 (((𝜑 → (¬ 𝜓𝜒)) → (𝜑 → (¬ 𝜒𝜓))) → ((𝜑 → (¬ 𝜓𝜒)) → (¬ 𝜒 → (𝜑𝜓))))
31, 2ax-mp 5 1 ((𝜑 → (¬ 𝜓𝜒)) → (¬ 𝜒 → (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40422  ax-frege2 40423  ax-frege8 40441  ax-frege28 40462  ax-frege31 40466
This theorem is referenced by:  frege40  40475
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