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Theorem bdssexi 15039
Description: Bounded version of ssexi 4156. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdssexi.bd  |- BOUNDED  A
bdssexi.1  |-  B  e. 
_V
bdssexi.2  |-  A  C_  B
Assertion
Ref Expression
bdssexi  |-  A  e. 
_V

Proof of Theorem bdssexi
StepHypRef Expression
1 bdssexi.2 . 2  |-  A  C_  B
2 bdssexi.bd . . 3  |- BOUNDED  A
3 bdssexi.1 . . 3  |-  B  e. 
_V
42, 3bdssex 15038 . 2  |-  ( A 
C_  B  ->  A  e.  _V )
51, 4ax-mp 5 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 2160   _Vcvv 2752    C_ wss 3144  BOUNDED wbdc 14976
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-bdsep 15020
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-in 3150  df-ss 3157  df-bdc 14977
This theorem is referenced by: (None)
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