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Theorem ssun2 3301
Description: Subclass relationship for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
ssun2  |-  A  C_  ( B  u.  A
)

Proof of Theorem ssun2
StepHypRef Expression
1 ssun1 3300 . 2  |-  A  C_  ( A  u.  B
)
2 uncom 3281 . 2  |-  ( A  u.  B )  =  ( B  u.  A
)
31, 2sseqtri 3191 1  |-  A  C_  ( B  u.  A
)
Colors of variables: wff set class
Syntax hints:    u. cun 3129    C_ wss 3131
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 2741  df-un 3135  df-in 3137  df-ss 3144
This theorem is referenced by:  ssun4  3303  elun2  3305  unv  3462  un00  3471  snsspr2  3743  snsstp3  3746  unexb  4444  rnexg  4894  brtpos0  6255  ac6sfi  6900  caserel  7088  pnfxr  8012  ltrelxr  8020  un0mulcl  9212  fsumsplit  11417  fprodsplitdc  11606  cnfldcj  13501  lgsdir2lem3  14470  bdunexb  14711
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