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Theorem bdssex 9357
Description: Bounded version of ssex 3885. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdssex.bd BOUNDED
bdssex.1  _V
Assertion
Ref Expression
bdssex 
C_  _V

Proof of Theorem bdssex
StepHypRef Expression
1 df-ss 2925 . 2 
C_  i^i
2 bdssex.bd . . . 4 BOUNDED
3 bdssex.1 . . . 4  _V
42, 3bdinex2 9355 . . 3  i^i 
_V
5 eleq1 2097 . . 3  i^i  i^i  _V  _V
64, 5mpbii 136 . 2  i^i  _V
71, 6sylbi 114 1 
C_  _V
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390   _Vcvv 2551    i^i cin 2910    C_ wss 2911  BOUNDED wbdc 9295
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-bdsep 9339
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-bdc 9296
This theorem is referenced by:  bdssexi  9358  bdssexg  9359  bdfind  9406
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