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Theorem csbie 3700
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 2902 . 2 𝑥𝐶
3 csbie.2 . 2 (𝑥 = 𝐴𝐵 = 𝐶)
41, 2, 3csbief 3699 1 𝐴 / 𝑥𝐵 = 𝐶
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1632  wcel 2139  Vcvv 3340  csb 3674
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-v 3342  df-sbc 3577  df-csb 3675
This theorem is referenced by:  pofun  5203  eqerlem  7947  mptnn0fsuppd  13012  fsum  14670  fsumcnv  14723  fsumshftm  14732  fsum0diag2  14734  fprod  14890  fprodcnv  14932  bpolyval  14999  ruclem1  15179  odval  18173  psrass1lem  19599  mamufval  20413  pm2mpval  20822  isibl  23751  dfitg  23755  dvfsumlem2  24009  fsumdvdsmul  25141  disjxpin  29729  poimirlem1  33741  poimirlem5  33745  poimirlem15  33755  poimirlem16  33756  poimirlem17  33757  poimirlem19  33759  poimirlem20  33760  poimirlem22  33762  poimirlem24  33764  poimirlem28  33768  fphpd  37900  monotuz  38026  oddcomabszz  38029  fnwe2val  38139  fnwe2lem1  38140
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