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Theorem frege50 36962
Description: Closed form of jaoi 393. Proposition 50 of [Frege1879] p. 49. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege50 ((𝜑𝜓) → ((𝜒𝜓) → ((¬ 𝜑𝜒) → 𝜓)))

Proof of Theorem frege50
StepHypRef Expression
1 frege49 36961 . 2 ((¬ 𝜑𝜒) → ((𝜑𝜓) → ((𝜒𝜓) → 𝜓)))
2 frege17 36929 . 2 (((¬ 𝜑𝜒) → ((𝜑𝜓) → ((𝜒𝜓) → 𝜓))) → ((𝜑𝜓) → ((𝜒𝜓) → ((¬ 𝜑𝜒) → 𝜓))))
31, 2ax-mp 5 1 ((𝜑𝜓) → ((𝜒𝜓) → ((¬ 𝜑𝜒) → 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 36898  ax-frege2 36899  ax-frege8 36917  ax-frege28 36938  ax-frege31 36942  ax-frege41 36953
This theorem is referenced by:  frege51  36963
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