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Theorem elun1 3317
Description: Membership law for union of classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elun1 (𝐴𝐵𝐴 ∈ (𝐵𝐶))

Proof of Theorem elun1
StepHypRef Expression
1 ssun1 3313 . 2 𝐵 ⊆ (𝐵𝐶)
21sseli 3166 1 (𝐴𝐵𝐴 ∈ (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2160  cun 3142
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157
This theorem is referenced by:  dcun  3548  exmidundif  4224  exmidundifim  4225  brtposg  6278  dftpos4  6287  dcdifsnid  6528  undifdcss  6950  fidcenumlemrks  6981  djulclr  7077  djulcl  7079  djuss  7098  finomni  7167  hashennnuni  10790  sumsplitdc  11471  srngbased  12655  srngplusgd  12656  srngmulrd  12657  lmodbased  12673  lmodplusgd  12674  lmodscad  12675  ipsbased  12685  ipsaddgd  12686  ipsmulrd  12687  psrbasg  13948
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