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Theorem bdssexi 10023
 Description: Bounded version of ssexi 3895. (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 10022 . 2 (𝐴𝐵𝐴 ∈ V)
51, 4ax-mp 7 1 𝐴 ∈ V
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1393  Vcvv 2557   ⊆ wss 2917  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-ss 2931  df-bdc 9961 This theorem is referenced by: (None)
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