Theorem ctex 6842

Description: A class dominated by om is a set. See also ctfoex 7220 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

Step	Hyp	Ref	Expression
1		reldom 6832	. 2 |- Rel ~<_
2	1	brrelex1i 4718	1 |- ( A ~<_ om -> A e. _V )

Syntax hints:   -> wi 4   e. wcel 2176   _Vcvv 2772   class class class wbr 4044   omcom 4638   ~<_ cdom 6826

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-14 2179  ax-ext 2187  ax-sep 4162  ax-pow 4218  ax-pr 4253

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-ral 2489  df-rex 2490  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-pw 3618  df-sn 3639  df-pr 3640  df-op 3642  df-br 4045  df-opab 4106  df-xp 4681  df-rel 4682  df-dom 6829

This theorem is referenced by:  cnvct  6901  ssct  6913  xpct  12767