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Theorem bdssexi 11136
Description: Bounded version of ssexi 3942. (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 11135 . 2  |-  ( A 
C_  B  ->  A  e.  _V )
51, 4ax-mp 7 1  |-  A  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   _Vcvv 2612    C_ wss 2984  BOUNDED wbdc 11073
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-bdsep 11117
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-in 2990  df-ss 2997  df-bdc 11074
This theorem is referenced by: (None)
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