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Theorem unjust 3479
 Description: Soundness justification theorem for df-un 3480. (Contributed by Rodolfo Medina, 28-Apr-2010.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
unjust
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem unjust
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2529 . . . 4
2 eleq1 2529 . . . 4
31, 2orbi12d 709 . . 3
43cbvabv 2600 . 2
5 eleq1 2529 . . . 4
6 eleq1 2529 . . . 4
75, 6orbi12d 709 . . 3
87cbvabv 2600 . 2
94, 8eqtri 2486 1
 Colors of variables: wff setvar class Syntax hints:  \/wo 368  =wceq 1395  e.wcel 1818  {cab 2442 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  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452
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