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Theorem csbie 3046
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 2282 . 2  |-  F/_ x C
3 csbie.2 . 2  |-  ( x  =  A  ->  B  =  C )
41, 2, 3csbief 3045 1  |-  [_ A  /  x ]_ B  =  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1332    e. wcel 1481   _Vcvv 2687   [_csb 3004
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2689  df-sbc 2911  df-csb 3005
This theorem is referenced by:  fsumcnv  11234  fisum0diag2  11244
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