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Theorem frege38 40473
Description: Identical to pm2.21 123. Proposition 38 of [Frege1879] p. 46. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege38 𝜑 → (𝜑𝜓))

Proof of Theorem frege38
StepHypRef Expression
1 frege36 40471 . 2 (𝜑 → (¬ 𝜑𝜓))
2 ax-frege8 40441 . 2 ((𝜑 → (¬ 𝜑𝜓)) → (¬ 𝜑 → (𝜑𝜓)))
31, 2ax-mp 5 1 𝜑 → (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-frege1 40422  ax-frege2 40423  ax-frege8 40441  ax-frege28 40462  ax-frege31 40466
This theorem is referenced by:  frege39  40474
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