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Theorem onuniss2 4357
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 3709 1 (𝐴 ∈ On → {𝑥 ∈ On ∣ 𝑥𝐴} = 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1296  wcel 1445  {crab 2374  wss 3013   cuni 3675  Oncon0 4214
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077
This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-rab 2379  df-v 2635  df-in 3019  df-ss 3026  df-uni 3676
This theorem is referenced by: (None)
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