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Theorem elun1 3372
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 3368 . 2 𝐵 ⊆ (𝐵𝐶)
21sseli 3221 1 (𝐴𝐵𝐴 ∈ (𝐵𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2200  cun 3196
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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211
This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2802  df-un 3202  df-in 3204  df-ss 3211
This theorem is referenced by:  dcun  3602  exmidundif  4294  exmidundifim  4295  brtposg  6415  dftpos4  6424  dcdifsnid  6667  elssdc  7087  undifdcss  7108  fidcenumlemrks  7143  djulclr  7239  djulcl  7241  djuss  7260  finomni  7330  hashennnuni  11031  sumsplitdc  11983  bassetsnn  13129  srngbased  13220  srngplusgd  13221  srngmulrd  13222  lmodbased  13238  lmodplusgd  13239  lmodscad  13240  ipsbased  13250  ipsaddgd  13251  ipsmulrd  13252  psrbasg  14678  elplyd  15455  ply1term  15457
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