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Theorem csbie 3117
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 2332 . 2 𝑥𝐶
3 csbie.2 . 2 (𝑥 = 𝐴𝐵 = 𝐶)
41, 2, 3csbief 3116 1 𝐴 / 𝑥𝐵 = 𝐶
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1364  wcel 2160  Vcvv 2752  csb 3072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-sbc 2978  df-csb 3073
This theorem is referenced by:  fsumcnv  11476  fisum0diag2  11486  fprodcnv  11664
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