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Theorem ssun2 3314
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 3313 . 2  |-  A  C_  ( A  u.  B
)
2 uncom 3294 . 2  |-  ( A  u.  B )  =  ( B  u.  A
)
31, 2sseqtri 3204 1  |-  A  C_  ( B  u.  A
)
Colors of variables: wff set class
Syntax hints:    u. cun 3142    C_ wss 3144
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157
This theorem is referenced by:  ssun4  3316  elun2  3318  unv  3475  un00  3484  snsspr2  3756  snsstp3  3759  unexb  4460  rnexg  4910  brtpos0  6278  ac6sfi  6927  caserel  7117  pnfxr  8041  ltrelxr  8049  un0mulcl  9241  fsumsplit  11450  fprodsplitdc  11639  lspun  13735  cnfldcj  13888  lgsdir2lem3  14909  bdunexb  15150
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