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Theorem bdssexd 9290
Description: Bounded version of ssexd 3888. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdssexd.1 (φB 𝐶)
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 (φB 𝐶)
3 bdssexd.bd . . 3 BOUNDED A
43bdssexg 9289 . 2 ((AB B 𝐶) → A V)
51, 2, 4syl2anc 391 1 (φA V)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  Vcvv 2551  wss 2911  BOUNDED wbdc 9229
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-bdsep 9273
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-bdc 9230
This theorem is referenced by: (None)
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