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Theorem bdinex2 10020
Description: Bounded version of inex2 3892. (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 3129 . 2  |-  ( B  i^i  A )  =  ( A  i^i  B
)
2 bdinex2.bd . . 3  |- BOUNDED  B
3 bdinex2.1 . . 3  |-  A  e. 
_V
42, 3bdinex1 10019 . 2  |-  ( A  i^i  B )  e. 
_V
51, 4eqeltri 2110 1  |-  ( B  i^i  A )  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 1393   _Vcvv 2557    i^i cin 2916  BOUNDED wbdc 9960
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-bdsep 10004
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-bdc 9961
This theorem is referenced by:  bdssex  10022
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