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Theorem elun1 3671
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 3667 . 2  |-  B  C_  ( B  u.  C
)
21sseli 3500 1  |-  ( A  e.  B  ->  A  e.  ( B  u.  C
) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1767    u. cun 3474
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-un 3481  df-in 3483  df-ss 3490
This theorem is referenced by:  brtpos  6964  dftpos4  6974  domunsncan  7617  unxpdomlem2  7725  rankunb  8268  rankelun  8290  fin1a2lem10  8789  zornn0g  8885  xrsupexmnf  11496  xrinfmexpnf  11497  sumsplit  13546  prmreclem5  14297  lbsextlem3  17606  restntr  19477  1stckgenlem  19817  fbun  20104  filcon  20147  filuni  20149  alexsubALTlem4  20313  ovolfiniun  21675  volfiniun  21720  elplyd  22362  ply1term  22364  aannenlem2  22487  aalioulem2  22491  eengbas  23988  ecgrtg  23990  vdgrf  24602  gsumle  27461  altxpsspw  29232  mbfresfi  29666  itg2addnclem2  29672  ftc1anclem7  29701  ftc1anc  29703  comppfsc  29807  limcresiooub  31212  limcresioolb  31213  fourierdlem48  31483  fourierdlem49  31484  fourierdlem51  31486  fourierdlem54  31489  fourierdlem62  31497  fourierdlem71  31506  fourierdlem103  31538  fourierdlem104  31539  fourierdlem114  31549  fouriersw  31560  sucidALTVD  32768  sucidALT  32769  bnj1498  33214  hdmaplem1  36586  hdmap1eulem  36639
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