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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 ⊆ (𝐵𝐴)

Proof of Theorem ssun2
StepHypRef Expression
1 ssun1 3106 . 2 𝐴 ⊆ (𝐴𝐵)
2 uncom 3087 . 2 (𝐴𝐵) = (𝐵𝐴)
31, 2sseqtri 2977 1 𝐴 ⊆ (𝐵𝐴)
 Colors of variables: wff set class Syntax hints:   ∪ cun 2915   ⊆ 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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