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Theorem elun1 3302
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 3298 . 2  |-  B  C_  ( B  u.  C
)
21sseli 3151 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2148    u. cun 3127
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 2739  df-un 3133  df-in 3135  df-ss 3142
This theorem is referenced by:  dcun  3533  exmidundif  4206  exmidundifim  4207  brtposg  6254  dftpos4  6263  dcdifsnid  6504  undifdcss  6921  fidcenumlemrks  6951  djulclr  7047  djulcl  7049  djuss  7068  finomni  7137  hashennnuni  10758  sumsplitdc  11439  srngbased  12604  srngplusgd  12605  srngmulrd  12606  lmodbased  12622  lmodplusgd  12623  lmodscad  12624  ipsbased  12634  ipsaddgd  12635  ipsmulrd  12636
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