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Theorem bdinex2 13087
Description: Bounded version of inex2 4058. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdinex2.bd  |- BOUNDED  B
bdinex2.1  |-  A  e. 
_V
Assertion
Ref Expression
bdinex2  |-  ( B  i^i  A )  e. 
_V

Proof of Theorem bdinex2
StepHypRef Expression
1 incom 3263 . 2  |-  ( B  i^i  A )  =  ( A  i^i  B
)
2 bdinex2.bd . . 3  |- BOUNDED  B
3 bdinex2.1 . . 3  |-  A  e. 
_V
42, 3bdinex1 13086 . 2  |-  ( A  i^i  B )  e. 
_V
51, 4eqeltri 2210 1  |-  ( B  i^i  A )  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   _Vcvv 2681    i^i cin 3065  BOUNDED wbdc 13027
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-bdsep 13071
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-in 3072  df-bdc 13028
This theorem is referenced by:  bdssex  13089
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