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Theorem csbex 4721
Description: The existence of proper substitution into a class. (Contributed by NM, 7-Aug-2007.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) (Revised by NM, 17-Aug-2018.)
Hypothesis
Ref Expression
csbex.1 𝐵 ∈ V
Assertion
Ref Expression
csbex 𝐴 / 𝑥𝐵 ∈ V

Proof of Theorem csbex
StepHypRef Expression
1 csbexg 4720 . 2 (∀𝑥 𝐵 ∈ V → 𝐴 / 𝑥𝐵 ∈ V)
2 csbex.1 . 2 𝐵 ∈ V
31, 2mpg 1715 1 𝐴 / 𝑥𝐵 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 1977  Vcvv 3173  csb 3499
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-nul 4717
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-fal 1481  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-sbc 3403  df-csb 3500  df-dif 3543  df-nul 3875
This theorem is referenced by:  iunopeqop  4906  dfmpt2  7154  cantnfdm  8444  cantnff  8454  bpolylem  14618  ruclem1  14799  pcmpt  15434  cidffn  16162  issubc  16318  natffn  16432  fnxpc  16639  evlfcl  16685  odf  17779  itgfsum  23399  itgparts  23614  vmaf  24645  ttgval  25555  abfmpel  28835  msrf  30693  finxpreclem2  32403  poimirlem17  32596  poimirlem23  32602  poimirlem24  32603  unirep  32677  cdlemk40  35223  aomclem6  36647  rnghmfn  41680  rngchomrnghmresALTV  41788
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