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Theorem eujust 2277
 Description: A soundness justification theorem for df-eu 2279, showing that the definition is equivalent to itself with its dummy variable renamed. Note that and needn't be distinct variables. See eujustALT 2278 for a proof that provides an example of how it can be achieved through the use of dvelim 2052. (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 1748 . . . . 5
21bibi2d 318 . . . 4
32albidv 1689 . . 3
43cbvexv 1997 . 2
5 equequ2 1748 . . . . 5
65bibi2d 318 . . . 4
76albidv 1689 . . 3
87cbvexv 1997 . 2
94, 8bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184  wal 1377  wex 1596 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600 This theorem is referenced by: (None)
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