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Theorem ctex 8512
Description: A countable set 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 8503 . 2 Rel ≼
21brrelex1i 5601 1 (𝐴 ≼ ω → 𝐴 ∈ V)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2105  Vcvv 3492   class class class wbr 5057  ωcom 7569  cdom 8495
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790  ax-sep 5194  ax-nul 5201  ax-pr 5320
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-ral 3140  df-rex 3141  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564  df-br 5058  df-opab 5120  df-xp 5554  df-rel 5555  df-dom 8499
This theorem is referenced by:  cnvct  8574  ssct  8586  xpct  9430  iunfictbso  9528  unctb  9615  dmct  9934  fimact  9945  fnct  9947  mptct  9948  iunctb  9984  cctop  21542  1stcrestlem  21988  2ndcdisj2  21993  dis2ndc  21996  uniiccdif  24106  mptctf  30379  elsigagen2  31306  measvunilem  31370  measvunilem0  31371  measvuni  31372  sxbrsigalem1  31442  omssubadd  31457  carsggect  31475  pmeasadd  31482  mpct  41340  axccdom  41363
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