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Theorem elun2 3318
Description: Membership law for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
elun2 (𝐴𝐵𝐴 ∈ (𝐶𝐵))

Proof of Theorem elun2
StepHypRef Expression
1 ssun2 3314 . 2 𝐵 ⊆ (𝐶𝐵)
21sseli 3166 1 (𝐴𝐵𝐴 ∈ (𝐶𝐵))
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  dftpos4  6289  tfrlemibxssdm  6353  tfrlemi14d  6359  tfr1onlembxssdm  6369  tfr1onlemres  6375  tfrcllembxssdm  6382  tfrcllemres  6388  dcdifsnid  6530  findcard2d  6920  findcard2sd  6921  onunsnss  6946  undifdcss  6952  fisseneq  6961  fidcenumlemrks  6983  djurclr  7080  djurcl  7082  djuss  7100  finomni  7169  mnfxr  8045  hashinfuni  10792  fsumsplitsnun  11462  sumsplitdc  11475  modfsummodlem1  11499  exmidunben  12480  srnginvld  12664  lmodvscad  12682  ipsscad  12694  ipsvscad  12695  ipsipd  12696
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