MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  eujust Unicode version

Theorem eujust 2264
Description: A soundness justification theorem for df-eu 2266, showing that the definition is equivalent to itself with its dummy variable renamed. Note that and needn't be distinct variables. See eujustALT 2265 for a proof that provides an example of how it can be achieved through the use of dvelim 2039. (Contributed by NM, 11-Mar-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
eujust
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem eujust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 equequ2 1739 . . . . 5
21bibi2d 318 . . . 4
32albidv 1680 . . 3
43cbvexv 1984 . 2
5 equequ2 1739 . . . . 5
65bibi2d 318 . . . 4
76albidv 1680 . . 3
87cbvexv 1984 . 2
94, 8bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wal 1368  E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591
  Copyright terms: Public domain W3C validator