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Theorem eujust 2285
 Description: A soundness justification theorem for df-eu 2287, showing that the definition is equivalent to itself with its dummy variable renamed. Note that and needn't be distinct variables. See eujustALT 2286 for a proof that provides an example of how it can be achieved through the use of dvelim 2074. (Contributed by NM, 11-Mar-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
eujust
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem eujust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 equequ2 1699 . . . . 5
21bibi2d 311 . . . 4
32albidv 1636 . . 3
43cbvexv 1986 . 2
5 equequ2 1699 . . . . 5
65bibi2d 311 . . . 4
76albidv 1636 . . 3
87cbvexv 1986 . 2
94, 8bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178  wal 1550  wex 1551 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555
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