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Theorem onuniss2 4435
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 3777 1 (𝐴 ∈ On → {𝑥 ∈ On ∣ 𝑥𝐴} = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1332  wcel 1481  {crab 2421  wss 3075   cuni 3743  Oncon0 4292
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rab 2426  df-v 2691  df-in 3081  df-ss 3088  df-uni 3744
This theorem is referenced by: (None)
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