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Theorem elun1 3344
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 3340 . 2 𝐵 ⊆ (𝐵𝐶)
21sseli 3193 1 (𝐴𝐵𝐴 ∈ (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2177  cun 3168
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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188
This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-un 3174  df-in 3176  df-ss 3183
This theorem is referenced by:  dcun  3574  exmidundif  4261  exmidundifim  4262  brtposg  6358  dftpos4  6367  dcdifsnid  6608  undifdcss  7041  fidcenumlemrks  7076  djulclr  7172  djulcl  7174  djuss  7193  finomni  7263  hashennnuni  10956  sumsplitdc  11828  srngbased  13064  srngplusgd  13065  srngmulrd  13066  lmodbased  13082  lmodplusgd  13083  lmodscad  13084  ipsbased  13094  ipsaddgd  13095  ipsmulrd  13096  psrbasg  14521  elplyd  15298  ply1term  15300
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