Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege55a Structured version   Visualization version   GIF version

Theorem frege55a 37006
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 37002 . 2 if-(𝜑, 𝜑, ¬ 𝜑)
2 frege53a 36998 . 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 194  if-wif 1005
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege8 36947  ax-frege28 36968  ax-frege52a 36995  ax-frege54a 37000
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-ifp 1006
This theorem is referenced by:  frege55cor1a  37007
  Copyright terms: Public domain W3C validator