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Theorem unjust 2949
 Description: Soundness justification theorem for df-un 2950. (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 2116 . . . 4
2 eleq1 2116 . . . 4
31, 2orbi12d 717 . . 3
43cbvabv 2177 . 2
5 eleq1 2116 . . . 4
6 eleq1 2116 . . . 4
75, 6orbi12d 717 . . 3
87cbvabv 2177 . 2
94, 8eqtri 2076 1
 Colors of variables: wff set class Syntax hints:   wo 639   wceq 1259   wcel 1409  cab 2042 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052 This theorem is referenced by: (None)
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