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Theorem ssun2 3164
Description: Subclass relationship for union of classes. (Contributed by NM, 30-Aug-1993.)
Assertion
Ref Expression
ssun2 𝐴 ⊆ (𝐵𝐴)

Proof of Theorem ssun2
StepHypRef Expression
1 ssun1 3163 . 2 𝐴 ⊆ (𝐴𝐵)
2 uncom 3144 . 2 (𝐴𝐵) = (𝐵𝐴)
31, 2sseqtri 3058 1 𝐴 ⊆ (𝐵𝐴)
Colors of variables: wff set class
Syntax hints:  cun 2997  wss 2999
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-in 3005  df-ss 3012
This theorem is referenced by:  ssun4  3166  elun2  3168  unv  3320  un00  3329  snsspr2  3586  snsstp3  3589  unexb  4267  rnexg  4698  brtpos0  6017  ac6sfi  6612  caserel  6776  pnfxr  7538  ltrelxr  7545  un0mulcl  8705  fsumsplit  10797  bdunexb  11766
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