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Theorem bdrabexg 9291
Description: Bounded version of rabexg 3891. (Contributed by BJ, 19-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bdrabexg.bd BOUNDED φ
bdrabexg.bdc BOUNDED A
Assertion
Ref Expression
bdrabexg (A 𝑉 → {x Aφ} V)
Distinct variable group:   x,A
Allowed substitution hints:   φ(x)   𝑉(x)

Proof of Theorem bdrabexg
StepHypRef Expression
1 ssrab2 3019 . 2 {x Aφ} ⊆ A
2 bdrabexg.bdc . . . 4 BOUNDED A
3 bdrabexg.bd . . . 4 BOUNDED φ
42, 3bdcrab 9241 . . 3 BOUNDED {x Aφ}
54bdssexg 9289 . 2 (({x Aφ} ⊆ A A 𝑉) → {x Aφ} V)
61, 5mpan 400 1 (A 𝑉 → {x Aφ} V)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  {crab 2304  Vcvv 2551  wss 2911  BOUNDED wbd 9201  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-bd0 9202  ax-bdan 9204  ax-bdsb 9211  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-rab 2309  df-v 2553  df-in 2918  df-ss 2925  df-bdc 9230
This theorem is referenced by:  bj-inex  9292
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