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Theorem bdinex2 13475
Description: Bounded version of inex2 4099. (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 3299 . 2  |-  ( B  i^i  A )  =  ( A  i^i  B
)
2 bdinex2.bd . . 3  |- BOUNDED  B
3 bdinex2.1 . . 3  |-  A  e. 
_V
42, 3bdinex1 13474 . 2  |-  ( A  i^i  B )  e. 
_V
51, 4eqeltri 2230 1  |-  ( B  i^i  A )  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 2128   _Vcvv 2712    i^i cin 3101  BOUNDED wbdc 13415
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-bdsep 13459
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-in 3108  df-bdc 13416
This theorem is referenced by:  bdssex  13477
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