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Theorem ssun2 3210
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 3209 . 2  |-  A  C_  ( A  u.  B
)
2 uncom 3190 . 2  |-  ( A  u.  B )  =  ( B  u.  A
)
31, 2sseqtri 3101 1  |-  A  C_  ( B  u.  A
)
Colors of variables: wff set class
Syntax hints:    u. cun 3039    C_ wss 3041
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054
This theorem is referenced by:  ssun4  3212  elun2  3214  unv  3370  un00  3379  snsspr2  3639  snsstp3  3642  unexb  4333  rnexg  4774  brtpos0  6117  ac6sfi  6760  caserel  6940  pnfxr  7786  ltrelxr  7793  un0mulcl  8979  fsumsplit  11144  bdunexb  13045
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