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Theorem eujust 1899
Description: A soundness justification theorem for df-eu 1900, 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 1596 . . . . 5
21bibi2d 221 . . . 4
32albidv 1702 . . 3
43cbvexv 1792 . 2
5 equequ2 1596 . . . . 5
65bibi2d 221 . . . 4
76albidv 1702 . . 3
87cbvexv 1792 . 2
94, 8bitri 173 1
Colors of variables: wff set class
Syntax hints:   wb 98  wal 1240   wceq 1242  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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