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Theorem elun2 3515
Description: Membership law for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
elun2  |-  ( A  e.  B  ->  A  e.  ( C  u.  B
) )

Proof of Theorem elun2
StepHypRef Expression
1 ssun2 3511 . 2  |-  B  C_  ( C  u.  B
)
21sseli 3344 1  |-  ( A  e.  B  ->  A  e.  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725    u. cun 3318
This theorem is referenced by:  dftpos4  6498  tfrlem11  6649  cantnfp1lem1  7634  cantnfp1lem3  7636  tc2  7681  rankunb  7776  rankelun  7798  dfac2  8011  cfsmolem  8150  isfin4-3  8195  zornn0g  8385  mnfxr  10714  supxrun  10894  sumsplit  12552  prmreclem5  13288  acsfiindd  14603  lspsolv  16215  mplcoe1  16528  restntr  17246  1stckgenlem  17585  fbun  17872  filuni  17917  ufileu  17951  alexsubALTlem4  18081  tmdgsum  18125  icccmplem2  18854  aannenlem2  20246  aalioulem2  20250  wfrlem14  25551  altxpsspw  25822  mbfresfi  26253  itg2addnclem2  26257  ftc1anclem7  26286  ftc1anc  26288  sucidVD  28984  bnj553  29269  bnj966  29315  bnj1442  29418  hdmaplem2N  32570  hdmaplem3  32571
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-in 3327  df-ss 3334
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