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Theorem bdrabexg 7129
 Description: Bounded version of rabexg 3874. (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 3002 . 2 {x Aφ} ⊆ A
2 bdrabexg.bdc . . . 4 BOUNDED A
3 bdrabexg.bd . . . 4 BOUNDED φ
42, 3bdcrab 7079 . . 3 BOUNDED {x Aφ}
54bdssexg 7127 . 2 (({x Aφ} ⊆ A A 𝑉) → {x Aφ} V)
61, 5mpan 402 1 (A 𝑉 → {x Aφ} V)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1374  {crab 2288  Vcvv 2535   ⊆ wss 2894  BOUNDED wbd 7039  BOUNDED wbdc 7067 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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-bd0 7040  ax-bdan 7042  ax-bdsb 7049  ax-bdsep 7111 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rab 2293  df-v 2537  df-in 2901  df-ss 2908  df-bdc 7068 This theorem is referenced by:  bj-inex  7130
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