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Theorem csbex 4956
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 4955 . 2 (∀𝑥 𝐵 ∈ V → 𝐴 / 𝑥𝐵 ∈ V)
2 csbex.1 . 2 𝐵 ∈ V
31, 2mpg 1892 1 𝐴 / 𝑥𝐵 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2155  Vcvv 3350  csb 3693
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2352  ax-ext 2743  ax-nul 4951
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-fal 1666  df-ex 1875  df-nf 1879  df-sb 2063  df-clab 2752  df-cleq 2758  df-clel 2761  df-nfc 2896  df-v 3352  df-sbc 3599  df-csb 3694  df-dif 3737  df-nul 4082
This theorem is referenced by:  iunopeqop  5144  dfmpt2  7471  cantnfdm  8778  cantnff  8788  bpolylem  15064  ruclem1  15245  pcmpt  15878  cidffn  16607  issubc  16763  natffn  16877  fnxpc  17085  evlfcl  17131  odf  18223  itgfsum  23887  itgparts  24104  vmaf  25139  ttgval  26049  abfmpel  29908  msrf  31890  finxpreclem2  33663  cnfinltrel  33677  poimirlem17  33853  poimirlem23  33859  poimirlem24  33860  unirep  33933  cdlemk40  36876  aomclem6  38309  rnghmfn  42562  rngchomrnghmresALTV  42668
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