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Theorem uneqri 3085
 Description: Inference from membership to union. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
uneqri.1
Assertion
Ref Expression
uneqri
Distinct variable groups:   ,   ,   ,

Proof of Theorem uneqri
StepHypRef Expression
1 elun 3084 . . 3
2 uneqri.1 . . 3
31, 2bitri 173 . 2
43eqriv 2037 1
 Colors of variables: wff set class Syntax hints:   wb 98   wo 629   wceq 1243   wcel 1393   cun 2915 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922 This theorem is referenced by:  unidm  3086  uncom  3087  unass  3100  undi  3185  unab  3204  un0  3251
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