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Theorem onuniss2 4160
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 3566 1 (A On → {x On ∣ xA} = A)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1373   wcel 1375  {crab 2286  wss 2895   cuni 3532  Oncon0 4024
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 1315  ax-7 1316  ax-gen 1317  ax-ie1 1362  ax-ie2 1363  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 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1329  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-ral 2287  df-rab 2291  df-v 2535  df-in 2902  df-ss 2909  df-uni 3533
This theorem is referenced by: (None)
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