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Theorem elun2 3304
Description: Membership law for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
elun2  |-  ( A  e.  B  ->  A  e.  ( C  u.  B
) )

Proof of Theorem elun2
StepHypRef Expression
1 ssun2 3300 . 2  |-  B  C_  ( C  u.  B
)
21sseli 3152 1  |-  ( A  e.  B  ->  A  e.  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2148    u. cun 3128
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-un 3134  df-in 3136  df-ss 3143
This theorem is referenced by:  dcun  3534  exmidundif  4207  exmidundifim  4208  dftpos4  6264  tfrlemibxssdm  6328  tfrlemi14d  6334  tfr1onlembxssdm  6344  tfr1onlemres  6350  tfrcllembxssdm  6357  tfrcllemres  6363  dcdifsnid  6505  findcard2d  6891  findcard2sd  6892  onunsnss  6916  undifdcss  6922  fisseneq  6931  fidcenumlemrks  6952  djurclr  7049  djurcl  7051  djuss  7069  finomni  7138  mnfxr  8014  hashinfuni  10757  fsumsplitsnun  11427  sumsplitdc  11440  modfsummodlem1  11464  exmidunben  12427  srnginvld  12608  lmodvscad  12626  ipsscad  12638  ipsvscad  12639  ipsipd  12640
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