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Theorem csbie 3524
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 2750 . 2 𝑥𝐶
3 csbie.2 . 2 (𝑥 = 𝐴𝐵 = 𝐶)
41, 2, 3csbief 3523 1 𝐴 / 𝑥𝐵 = 𝐶
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1474  wcel 1976  Vcvv 3172  csb 3498
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-3an 1032  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-v 3174  df-sbc 3402  df-csb 3499
This theorem is referenced by:  pofun  4965  eqerlem  7641  mptnn0fsuppd  12618  fsum  14247  fsumcnv  14295  fsumshftm  14304  fsum0diag2  14306  fprod  14459  fprodcnv  14501  bpolyval  14568  ruclem1  14748  odval  17725  psrass1lem  19147  mamufval  19958  pm2mpval  20367  isibl  23283  dfitg  23287  dvfsumlem2  23539  fsumdvdsmul  24666  disjxpin  28617  poimirlem1  32404  poimirlem5  32408  poimirlem15  32418  poimirlem16  32419  poimirlem17  32420  poimirlem19  32422  poimirlem20  32423  poimirlem22  32425  poimirlem24  32427  poimirlem28  32431  fphpd  36222  monotuz  36348  oddcomabszz  36351  fnwe2val  36461  fnwe2lem1  36462
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