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Theorem frege39 37156
Description: Syllogism between pm2.18 121 and pm2.24 120. 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 37155 . 2 𝜑 → (𝜑𝜓))
2 ax-frege2 37105 . 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 37104  ax-frege2 37105  ax-frege8 37123  ax-frege28 37144  ax-frege31 37148
This theorem is referenced by:  frege40  37157
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