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Theorem frege57a 38484
Description: Analogue of frege57aid 38483. Proposition 57 of [Frege1879] p. 51. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege57a ((𝜑𝜓) → (if-(𝜓, 𝜒, 𝜃) → if-(𝜑, 𝜒, 𝜃)))

Proof of Theorem frege57a
StepHypRef Expression
1 ax-frege52a 38468 . 2 ((𝜓𝜑) → (if-(𝜓, 𝜒, 𝜃) → if-(𝜑, 𝜒, 𝜃)))
2 frege56a 38482 . 2 (((𝜓𝜑) → (if-(𝜓, 𝜒, 𝜃) → if-(𝜑, 𝜒, 𝜃))) → ((𝜑𝜓) → (if-(𝜓, 𝜒, 𝜃) → if-(𝜑, 𝜒, 𝜃))))
31, 2ax-mp 5 1 ((𝜑𝜓) → (if-(𝜓, 𝜒, 𝜃) → if-(𝜑, 𝜒, 𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  if-wif 1032
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege1 38401  ax-frege2 38402  ax-frege8 38420  ax-frege28 38441  ax-frege52a 38468  ax-frege54a 38473
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ifp 1033
This theorem is referenced by: (None)
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