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Theorem csbie 3525
 Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by AV, 2-Dec-2019.)
Hypotheses
Ref Expression
csbie.1 𝐴 ∈ V
csbie.2 (𝑥 = 𝐴𝐵 = 𝐶)
Assertion
Ref Expression
csbie 𝐴 / 𝑥𝐵 = 𝐶
Distinct variable groups:   𝑥,𝐴   𝑥,𝐶
Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem csbie
StepHypRef Expression
1 csbie.1 . 2 𝐴 ∈ V
2 nfcv 2751 . 2 𝑥𝐶
3 csbie.2 . 2 (𝑥 = 𝐴𝐵 = 𝐶)
41, 2, 3csbief 3524 1 𝐴 / 𝑥𝐵 = 𝐶
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475   ∈ 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 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  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 This theorem is referenced by:  pofun  4975  eqerlem  7663  mptnn0fsuppd  12660  fsum  14298  fsumcnv  14346  fsumshftm  14355  fsum0diag2  14357  fprod  14510  fprodcnv  14552  bpolyval  14619  ruclem1  14799  odval  17776  psrass1lem  19198  mamufval  20010  pm2mpval  20419  isibl  23338  dfitg  23342  dvfsumlem2  23594  fsumdvdsmul  24721  disjxpin  28783  poimirlem1  32580  poimirlem5  32584  poimirlem15  32594  poimirlem16  32595  poimirlem17  32596  poimirlem19  32598  poimirlem20  32599  poimirlem22  32601  poimirlem24  32603  poimirlem28  32607  fphpd  36398  monotuz  36524  oddcomabszz  36527  fnwe2val  36637  fnwe2lem1  36638
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