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Theorem frege53aid 36967
Description: Specialization of frege53a 36968. 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 36966 . 2 ((𝜑𝜓) → (𝜑𝜓))
2 ax-frege8 36917 . 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 195
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 36917  ax-frege52a 36965
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-ifp 1007  df-tru 1478  df-fal 1481
This theorem is referenced by: (None)
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