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Theorem unjust 3082
 Description: Soundness justification theorem for df-un 3083. (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
StepHypRef Expression
1 eleq1 2313 . . . 4
2 eleq1 2313 . . . 4
31, 2orbi12d 693 . . 3
43cbvabv 2368 . 2
5 eleq1 2313 . . . 4
6 eleq1 2313 . . . 4
75, 6orbi12d 693 . . 3
87cbvabv 2368 . 2
94, 8eqtri 2273 1
 Colors of variables: wff set class Syntax hints:   wo 359   wceq 1619   wcel 1621  cab 2239 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249
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