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Theorem frege56aid 40502
Description: Lemma for frege57aid 40504. Proposition 56 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege56aid (((𝜑𝜓) → (𝜑𝜓)) → ((𝜓𝜑) → (𝜑𝜓)))

Proof of Theorem frege56aid
StepHypRef Expression
1 frege55aid 40497 . 2 ((𝜓𝜑) → (𝜑𝜓))
2 frege9 40444 . 2 (((𝜓𝜑) → (𝜑𝜓)) → (((𝜑𝜓) → (𝜑𝜓)) → ((𝜓𝜑) → (𝜑𝜓))))
31, 2ax-mp 5 1 (((𝜑𝜓) → (𝜑𝜓)) → ((𝜓𝜑) → (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 209
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 40422  ax-frege2 40423  ax-frege8 40441
This theorem depends on definitions:  df-bi 210
This theorem is referenced by:  frege57aid  40504
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