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Theorem ssun2 3299
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 3298 . 2  |-  A  C_  ( A  u.  B
)
2 uncom 3279 . 2  |-  ( A  u.  B )  =  ( B  u.  A
)
31, 2sseqtri 3189 1  |-  A  C_  ( B  u.  A
)
Colors of variables: wff set class
Syntax hints:    u. cun 3127    C_ wss 3129
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:  ssun4  3301  elun2  3303  unv  3460  un00  3469  snsspr2  3741  snsstp3  3744  unexb  4442  rnexg  4892  brtpos0  6252  ac6sfi  6897  caserel  7085  pnfxr  8009  ltrelxr  8017  un0mulcl  9209  fsumsplit  11414  fprodsplitdc  11603  cnfldcj  13432  lgsdir2lem3  14401  bdunexb  14642
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