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Theorem csbie 2973
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 2228 . 2  |-  F/_ x C
3 csbie.2 . 2  |-  ( x  =  A  ->  B  =  C )
41, 2, 3csbief 2972 1  |-  [_ A  /  x ]_ B  =  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1289    e. wcel 1438   _Vcvv 2619   [_csb 2933
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-sbc 2841  df-csb 2934
This theorem is referenced by:  fsumcnv  10827  fisum0diag2  10837
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