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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  e. 
_V
csbie.2  |-  ( x  =  A  ->  B  =  C )
Assertion
Ref Expression
csbie  |-  [_ A  /  x ]_ B  =  C
Distinct variable groups:    x, A    x, C
Allowed substitution hint:    B( x)

Proof of Theorem csbie
StepHypRef Expression
1 csbie.1 . 2  |-  A  e. 
_V
2 nfcv 2332 . 2  |-  F/_ x C
3 csbie.2 . 2  |-  ( x  =  A  ->  B  =  C )
41, 2, 3csbief 3116 1  |-  [_ A  /  x ]_ B  =  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1364    e. 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  11480  fisum0diag2  11490  fprodcnv  11668
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