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Theorem ctex 6654
Description: A class dominated by  om is a set. See also ctfoex 7010 which says that a countable class is a set. (Contributed by Thierry Arnoux, 29-Dec-2016.) (Proof shortened by Jim Kingdon, 13-Mar-2023.)
Assertion
Ref Expression
ctex  |-  ( A  ~<_  om  ->  A  e.  _V )

Proof of Theorem ctex
StepHypRef Expression
1 reldom 6646 . 2  |-  Rel  ~<_
21brrelex1i 4589 1  |-  ( A  ~<_  om  ->  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1481   _Vcvv 2689   class class class wbr 3936   omcom 4511    ~<_ cdom 6640
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-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4053  ax-pow 4105  ax-pr 4138
This theorem depends on definitions:  df-bi 116  df-3an 965  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-rex 2423  df-v 2691  df-un 3079  df-in 3081  df-ss 3088  df-pw 3516  df-sn 3537  df-pr 3538  df-op 3540  df-br 3937  df-opab 3997  df-xp 4552  df-rel 4553  df-dom 6643
This theorem is referenced by:  cnvct  6710  ssct  6719  xpct  11943
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