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Theorem eujust 1944
 Description: A soundness justification theorem for df-eu 1945, showing that the definition is equivalent to itself with its dummy variable renamed. Note that and needn't be distinct variables. (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 1640 . . . . 5
21bibi2d 230 . . . 4
32albidv 1746 . . 3
43cbvexv 1837 . 2
5 equequ2 1640 . . . . 5
65bibi2d 230 . . . 4
76albidv 1746 . . 3
87cbvexv 1837 . 2
94, 8bitri 182 1
 Colors of variables: wff set class Syntax hints:   wb 103  wal 1283   wceq 1285  wex 1422 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468 This theorem depends on definitions:  df-bi 115 This theorem is referenced by: (None)
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