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Theorem frege55lem2a 40091
Description: Core proof of Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege55lem2a ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))

Proof of Theorem frege55lem2a
StepHypRef Expression
1 bicom1 222 . 2 ((𝜑𝜓) → (𝜓𝜑))
2 frege54cor0a 40087 . 2 ((𝜓𝜑) ↔ if-(𝜓, 𝜑, ¬ 𝜑))
31, 2sylib 219 1 ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207  if-wif 1054
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege28 40054
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-ifp 1055
This theorem is referenced by: (None)
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