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Theorem frege43 37161
Description: If there is a choice only between 𝜑 and 𝜑, then 𝜑 takes place. Identical to pm2.18 121. 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 37160 . 2 ¬ ¬ (𝜑𝜑)
2 frege40 37157 . 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 37104  ax-frege2 37105  ax-frege8 37123  ax-frege28 37144  ax-frege31 37148  ax-frege41 37159
This theorem is referenced by:  frege44  37162
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