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Theorem bdinex2 11791
Description: Bounded version of inex2 3974. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdinex2.bd BOUNDED 𝐵
bdinex2.1 𝐴 ∈ V
Assertion
Ref Expression
bdinex2 (𝐵𝐴) ∈ V

Proof of Theorem bdinex2
StepHypRef Expression
1 incom 3192 . 2 (𝐵𝐴) = (𝐴𝐵)
2 bdinex2.bd . . 3 BOUNDED 𝐵
3 bdinex2.1 . . 3 𝐴 ∈ V
42, 3bdinex1 11790 . 2 (𝐴𝐵) ∈ V
51, 4eqeltri 2160 1 (𝐵𝐴) ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1438  Vcvv 2619  cin 2998  BOUNDED wbdc 11731
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-bdsep 11775
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-in 3005  df-bdc 11732
This theorem is referenced by:  bdssex  11793
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