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Theorem elun1 3482
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 3478 . 2  |-  B  C_  ( B  u.  C
)
21sseli 3312 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1721    u. cun 3286
This theorem is referenced by:  brtpos  6455  dftpos4  6465  domunsncan  7175  unxpdomlem2  7281  rankunb  7740  rankelun  7762  fin1a2lem10  8253  zornn0g  8349  xrsupexmnf  10847  xrinfmexpnf  10848  sumsplit  12515  prmreclem5  13251  lbsextlem3  16195  restntr  17208  1stckgenlem  17546  fbun  17833  filcon  17876  filuni  17878  alexsubALTlem4  18042  ovolfiniun  19358  volfiniun  19402  elplyd  20082  ply1term  20084  aannenlem2  20207  aalioulem2  20211  vdgrf  21630  altxpsspw  25734  mbfresfi  26160  itg2addnclem2  26164  comppfsc  26285  sucidALTVD  28700  sucidALT  28701  bnj1498  29148  hdmaplem1  32266  hdmap1eulem  32319
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-un 3293  df-in 3295  df-ss 3302
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