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Theorem elun1 3274
Description: Membership law for union of classes. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
elun1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )

Proof of Theorem elun1
StepHypRef Expression
1 ssun1 3270 . 2  |-  B  C_  ( B  u.  C
)
21sseli 3124 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2128    u. cun 3100
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-in 3108  df-ss 3115
This theorem is referenced by:  dcun  3504  exmidundif  4168  exmidundifim  4169  brtposg  6202  dftpos4  6211  dcdifsnid  6452  undifdcss  6868  fidcenumlemrks  6898  djulclr  6994  djulcl  6996  djuss  7015  finomni  7084  hashennnuni  10657  sumsplitdc  11333  srngbased  12355  srngplusgd  12356  srngmulrd  12357  lmodbased  12366  lmodplusgd  12367  lmodscad  12368  ipsbased  12374  ipsaddgd  12375  ipsmulrd  12376
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