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Theorem bdssexd 13030
Description: Bounded version of ssexd 4038. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdssexd.1  |-  ( ph  ->  B  e.  C )
bdssexd.2  |-  ( ph  ->  A  C_  B )
bdssexd.bd  |- BOUNDED  A
Assertion
Ref Expression
bdssexd  |-  ( ph  ->  A  e.  _V )

Proof of Theorem bdssexd
StepHypRef Expression
1 bdssexd.2 . 2  |-  ( ph  ->  A  C_  B )
2 bdssexd.1 . 2  |-  ( ph  ->  B  e.  C )
3 bdssexd.bd . . 3  |- BOUNDED  A
43bdssexg 13029 . 2  |-  ( ( A  C_  B  /\  B  e.  C )  ->  A  e.  _V )
51, 2, 4syl2anc 408 1  |-  ( ph  ->  A  e.  _V )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1465   _Vcvv 2660    C_ wss 3041  BOUNDED wbdc 12965
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-bdsep 13009
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-in 3047  df-ss 3054  df-bdc 12966
This theorem is referenced by: (None)
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