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Theorem frege55cor1a 37666
Description: Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege55cor1a ((𝜑𝜓) → (𝜓𝜑))

Proof of Theorem frege55cor1a
StepHypRef Expression
1 frege55a 37665 . 2 ((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))
2 frege55lem1a 37663 . 2 (((𝜑𝜓) → if-(𝜓, 𝜑, ¬ 𝜑)) → ((𝜑𝜓) → (𝜓𝜑)))
31, 2ax-mp 5 1 ((𝜑𝜓) → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  if-wif 1011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 37606  ax-frege28 37627  ax-frege52a 37654  ax-frege54a 37659
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ifp 1012
This theorem is referenced by:  frege56a  37668
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