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Theorem elun1 3342
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 3338 . 2  |-  B  C_  ( B  u.  C
)
21sseli 3176 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1684    u. cun 3150
This theorem is referenced by:  brtpos  6243  dftpos4  6253  domunsncan  6962  unxpdomlem2  7068  rankunb  7522  rankelun  7544  fin1a2lem10  8035  zornn0g  8132  xrsupexmnf  10623  xrinfmexpnf  10624  sumsplit  12231  prmreclem5  12967  lbsextlem3  15913  restntr  16912  1stckgenlem  17248  fbun  17535  filcon  17578  filuni  17580  alexsubALTlem4  17744  ovolfiniun  18860  volfiniun  18904  elplyd  19584  ply1term  19586  aannenlem2  19709  aalioulem2  19713  altxpsspw  24511  basexre  25522  pgapspf  26052  comppfsc  26307  sucidALTVD  28646  sucidALT  28647  bnj1498  29091  hdmaplem1  31961  hdmap1eulem  32014
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-in 3159  df-ss 3166
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