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Theorem bdssexi 12924
Description: Bounded version of ssexi 4034. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdssexi.bd BOUNDED 𝐴
bdssexi.1 𝐵 ∈ V
bdssexi.2 𝐴𝐵
Assertion
Ref Expression
bdssexi 𝐴 ∈ V

Proof of Theorem bdssexi
StepHypRef Expression
1 bdssexi.2 . 2 𝐴𝐵
2 bdssexi.bd . . 3 BOUNDED 𝐴
3 bdssexi.1 . . 3 𝐵 ∈ V
42, 3bdssex 12923 . 2 (𝐴𝐵𝐴 ∈ V)
51, 4ax-mp 5 1 𝐴 ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1463  Vcvv 2658  wss 3039  BOUNDED wbdc 12861
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-bdsep 12905
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-in 3045  df-ss 3052  df-bdc 12862
This theorem is referenced by: (None)
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