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Theorem elun1 3243
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 3239 . 2  |-  B  C_  ( B  u.  C
)
21sseli 3093 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1480    u. cun 3069
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084
This theorem is referenced by:  dcun  3473  exmidundif  4129  exmidundifim  4130  brtposg  6151  dftpos4  6160  dcdifsnid  6400  undifdcss  6811  fidcenumlemrks  6841  djulclr  6934  djulcl  6936  djuss  6955  finomni  7012  hashennnuni  10532  sumsplitdc  11208  srngbased  12092  srngplusgd  12093  srngmulrd  12094  lmodbased  12103  lmodplusgd  12104  lmodscad  12105  ipsbased  12111  ipsaddgd  12112  ipsmulrd  12113
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