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Theorem frege55a 37182
Description: Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege55a ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))

Proof of Theorem frege55a
StepHypRef Expression
1 frege54cor1a 37178 . 2 if-(𝜑, 𝜑, ¬ 𝜑)
2 frege53a 37174 . 2 (if-(𝜑, 𝜑, ¬ 𝜑) → ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑)))
31, 2ax-mp 5 1 ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 195  if-wif 1006
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 37123  ax-frege28 37144  ax-frege52a 37171  ax-frege54a 37176
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-ifp 1007
This theorem is referenced by:  frege55cor1a  37183
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