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Theorem bdssexd 13680
Description: Bounded version of ssexd 4119. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdssexd.1 (𝜑𝐵𝐶)
bdssexd.2 (𝜑𝐴𝐵)
bdssexd.bd BOUNDED 𝐴
Assertion
Ref Expression
bdssexd (𝜑𝐴 ∈ V)

Proof of Theorem bdssexd
StepHypRef Expression
1 bdssexd.2 . 2 (𝜑𝐴𝐵)
2 bdssexd.1 . 2 (𝜑𝐵𝐶)
3 bdssexd.bd . . 3 BOUNDED 𝐴
43bdssexg 13679 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
51, 2, 4syl2anc 409 1 (𝜑𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2135  Vcvv 2724  wss 3114  BOUNDED wbdc 13615
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 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146  ax-bdsep 13659
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-v 2726  df-in 3120  df-ss 3127  df-bdc 13616
This theorem is referenced by: (None)
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