Users' Mathboxes Mathbox for Richard Penner < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  frege54cor1a Structured version   Visualization version   GIF version

Theorem frege54cor1a 37661
Description: Reflexive equality. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege54cor1a if-(𝜑, 𝜑, ¬ 𝜑)

Proof of Theorem frege54cor1a
StepHypRef Expression
1 ax-frege54a 37659 . 2 (𝜑𝜑)
2 frege54cor0a 37660 . 2 ((𝜑𝜑) ↔ if-(𝜑, 𝜑, ¬ 𝜑))
31, 2mpbi 220 1 if-(𝜑, 𝜑, ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  if-wif 1011
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-frege28 37627  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:  frege55a  37665
  Copyright terms: Public domain W3C validator