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Theorem bdinex2 13486
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 ∈ V
Assertion
Ref Expression
bdinex2 (𝐵𝐴) ∈ V

Proof of Theorem bdinex2
StepHypRef Expression
1 incom 3299 . 2 (𝐵𝐴) = (𝐴𝐵)
2 bdinex2.bd . . 3 BOUNDED 𝐵
3 bdinex2.1 . . 3 𝐴 ∈ V
42, 3bdinex1 13485 . 2 (𝐴𝐵) ∈ V
51, 4eqeltri 2230 1 (𝐵𝐴) ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 2128  Vcvv 2712  cin 3101  BOUNDED wbdc 13426
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 13470
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 13427
This theorem is referenced by:  bdssex  13488
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