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Theorem bdssexd 12937
Description: Bounded version of ssexd 4036. (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 12936 . 2 ((𝐴𝐵𝐵𝐶) → 𝐴 ∈ V)
51, 2, 4syl2anc 406 1 (𝜑𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1463  Vcvv 2658  wss 3039  BOUNDED wbdc 12872
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 12916
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 12873
This theorem is referenced by: (None)
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