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Theorem eujust 2284
Description: A soundness justification theorem for df-eu 2286, showing that the definition is equivalent to itself with its dummy variable renamed. Note that and needn't be distinct variables. See eujustALT 2285 for a proof that provides an example of how it can be achieved through the use of dvelim 2079. (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 1799 . . . . 5
21bibi2d 318 . . . 4
32albidv 1713 . . 3
43cbvexv 2024 . 2
5 equequ2 1799 . . . . 5
65bibi2d 318 . . . 4
76albidv 1713 . . 3
87cbvexv 2024 . 2
94, 8bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  A.wal 1393  E.wex 1612
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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