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Theorem frege53aid 40414
Description: Specialization of frege53a 40415. Proposition 53 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege53aid (𝜑 → ((𝜑𝜓) → 𝜓))

Proof of Theorem frege53aid
StepHypRef Expression
1 frege52aid 40413 . 2 ((𝜑𝜓) → (𝜑𝜓))
2 ax-frege8 40364 . 2 (((𝜑𝜓) → (𝜑𝜓)) → (𝜑 → ((𝜑𝜓) → 𝜓)))
31, 2ax-mp 5 1 (𝜑 → ((𝜑𝜓) → 𝜓))
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-frege8 40364  ax-frege52a 40412
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ifp 1059  df-tru 1541  df-fal 1551
This theorem is referenced by: (None)
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