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Theorem onuniss2 4526
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 3858 1 (𝐴 ∈ On → {𝑥 ∈ On ∣ 𝑥𝐴} = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1364  wcel 2160  {crab 2472  wss 3144   cuni 3824  Oncon0 4378
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rab 2477  df-v 2754  df-in 3150  df-ss 3157  df-uni 3825
This theorem is referenced by: (None)
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