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Theorem elun2 3141
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 3137 . 2  |-  B  C_  ( C  u.  B
)
21sseli 2996 1  |-  ( A  e.  B  ->  A  e.  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434    u. cun 2972
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978  df-in 2980  df-ss 2987
This theorem is referenced by:  dftpos4  5912  tfrlemibxssdm  5976  tfrlemi14d  5982  tfr1onlembxssdm  5992  tfr1onlemres  5998  tfrcllembxssdm  6005  tfrcllemres  6011  nndifsnid  6146  fidifsnid  6406  findcard2d  6425  findcard2sd  6426  onunsnss  6437  mnfxr  7237  sizeinfuni  9801
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