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Theorem frege40 36960
Description: Anything implies pm2.18 120. Proposition 40 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege40 𝜑 → ((¬ 𝜓𝜓) → 𝜓))

Proof of Theorem frege40
StepHypRef Expression
1 frege39 36959 . 2 ((¬ 𝜓𝜓) → (¬ 𝜓𝜑))
2 frege35 36955 . 2 (((¬ 𝜓𝜓) → (¬ 𝜓𝜑)) → (¬ 𝜑 → ((¬ 𝜓𝜓) → 𝜓)))
31, 2ax-mp 5 1 𝜑 → ((¬ 𝜓𝜓) → 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36907  ax-frege2 36908  ax-frege8 36926  ax-frege28 36947  ax-frege31 36951
This theorem is referenced by:  frege43  36964
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