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Theorem unjust 3284
 Description: Soundness justification theorem for df-un 3285. (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 2464 . . . 4
2 eleq1 2464 . . . 4
31, 2orbi12d 691 . . 3
43cbvabv 2523 . 2
5 eleq1 2464 . . . 4
6 eleq1 2464 . . . 4
75, 6orbi12d 691 . . 3
87cbvabv 2523 . 2
94, 8eqtri 2424 1
 Colors of variables: wff set class Syntax hints:   wo 358   wceq 1649   wcel 1721  cab 2390 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400
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