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Theorem ssun2 3107
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 3106 . 2  |-  A  C_  ( A  u.  B
)
2 uncom 3087 . 2  |-  ( A  u.  B )  =  ( B  u.  A
)
31, 2sseqtri 2977 1  |-  A  C_  ( B  u.  A
)
Colors of variables: wff set class
Syntax hints:    u. cun 2915    C_ wss 2917
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931
This theorem is referenced by:  ssun4  3109  elun2  3111  nsspssun  3170  unv  3254  un00  3263  snsspr2  3513  snsstp3  3516  unexb  4177  rnexg  4597  brtpos0  5867  ac6sfi  6352  ltrelxr  7080  un0mulcl  8216  pnfxr  8692  bdunexb  10040
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