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Theorem frege44 38983
Description: Similar to a commuted pm2.62 930. Proposition 44 of [Frege1879] p. 47. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege44 ((¬ 𝜑𝜓) → ((𝜓𝜑) → 𝜑))

Proof of Theorem frege44
StepHypRef Expression
1 frege43 38982 . 2 ((¬ 𝜑𝜑) → 𝜑)
2 frege21 38962 . 2 (((¬ 𝜑𝜑) → 𝜑) → ((¬ 𝜑𝜓) → ((𝜓𝜑) → 𝜑)))
31, 2ax-mp 5 1 ((¬ 𝜑𝜓) → ((𝜓𝜑) → 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 38925  ax-frege2 38926  ax-frege8 38944  ax-frege28 38965  ax-frege31 38969  ax-frege41 38980
This theorem is referenced by:  frege45  38984
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