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Theorem frege39 37956
Description: Syllogism between pm2.18 122 and pm2.24 121. Proposition 39 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege39 ((¬ 𝜑𝜑) → (¬ 𝜑𝜓))

Proof of Theorem frege39
StepHypRef Expression
1 frege38 37955 . 2 𝜑 → (𝜑𝜓))
2 ax-frege2 37905 . 2 ((¬ 𝜑 → (𝜑𝜓)) → ((¬ 𝜑𝜑) → (¬ 𝜑𝜓)))
31, 2ax-mp 5 1 ((¬ 𝜑𝜑) → (¬ 𝜑𝜓))
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  ax-frege31 37948
This theorem is referenced by:  frege40  37957
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