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Theorem ctex 6656
 Description: A class dominated by ω is a set. See also ctfoex 7013 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 ≼ ω → 𝐴 ∈ V)

Proof of Theorem ctex
StepHypRef Expression
1 reldom 6648 . 2 Rel ≼
21brrelex1i 4591 1 (𝐴 ≼ ω → 𝐴 ∈ V)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1481  Vcvv 2690   class class class wbr 3938  ωcom 4513   ≼ cdom 6642 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 4055  ax-pow 4107  ax-pr 4140 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 2692  df-un 3081  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539  df-pr 3540  df-op 3542  df-br 3939  df-opab 3999  df-xp 4554  df-rel 4555  df-dom 6645 This theorem is referenced by:  cnvct  6712  ssct  6721  xpct  11965
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