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Theorem frege43 36959
Description: If there is a choice only between 𝜑 and 𝜑, then 𝜑 takes place. Identical to pm2.18 120. Proposition 43 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege43 ((¬ 𝜑𝜑) → 𝜑)

Proof of Theorem frege43
StepHypRef Expression
1 frege42 36958 . 2 ¬ ¬ (𝜑𝜑)
2 frege40 36955 . 2 (¬ ¬ (𝜑𝜑) → ((¬ 𝜑𝜑) → 𝜑))
31, 2ax-mp 5 1 ((¬ 𝜑𝜑) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36902  ax-frege2 36903  ax-frege8 36921  ax-frege28 36942  ax-frege31 36946  ax-frege41 36957
This theorem is referenced by:  frege44  36960
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