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Theorem elun2 3303
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 3299 . 2  |-  B  C_  ( C  u.  B
)
21sseli 3151 1  |-  ( A  e.  B  ->  A  e.  ( C  u.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2148    u. cun 3127
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142
This theorem is referenced by:  dcun  3533  exmidundif  4205  exmidundifim  4206  dftpos4  6261  tfrlemibxssdm  6325  tfrlemi14d  6331  tfr1onlembxssdm  6341  tfr1onlemres  6347  tfrcllembxssdm  6354  tfrcllemres  6360  dcdifsnid  6502  findcard2d  6888  findcard2sd  6889  onunsnss  6913  undifdcss  6919  fisseneq  6928  fidcenumlemrks  6949  djurclr  7046  djurcl  7048  djuss  7066  finomni  7135  mnfxr  8010  hashinfuni  10750  fsumsplitsnun  11420  sumsplitdc  11433  modfsummodlem1  11457  exmidunben  12419  srnginvld  12600  lmodvscad  12618  ipsscad  12630  ipsvscad  12631  ipsipd  12632
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