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Theorem onuniss2 4185
Description: The union of the ordinal subsets of an ordinal number is that number. (Contributed by Jim Kingdon, 2-Aug-2019.)
Assertion
Ref Expression
onuniss2 (A On → {x On ∣ xA} = A)
Distinct variable group:   x,A

Proof of Theorem onuniss2
StepHypRef Expression
1 unimax 3587 1 (A On → {x On ∣ xA} = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1228   wcel 1375  {crab 2287  wss 2893   cuni 3553  Oncon0 4047
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1364  ax-ie2 1365  ax-8 1377  ax-10 1378  ax-11 1379  ax-i12 1380  ax-bnd 1381  ax-4 1382  ax-17 1401  ax-i9 1405  ax-ial 1410  ax-i5r 1411  ax-ext 2005
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1629  df-clab 2010  df-cleq 2016  df-clel 2019  df-nfc 2150  df-ral 2288  df-rab 2292  df-v 2536  df-in 2900  df-ss 2907  df-uni 3554
This theorem is referenced by: (None)
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