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Theorem elun1 3303
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 3299 . 2  |-  B  C_  ( B  u.  C
)
21sseli 3152 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
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  brtposg  6255  dftpos4  6264  dcdifsnid  6505  undifdcss  6922  fidcenumlemrks  6952  djulclr  7048  djulcl  7050  djuss  7069  finomni  7138  hashennnuni  10759  sumsplitdc  11440  srngbased  12605  srngplusgd  12606  srngmulrd  12607  lmodbased  12623  lmodplusgd  12624  lmodscad  12625  ipsbased  12635  ipsaddgd  12636  ipsmulrd  12637
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