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Theorem csbov2g 5816
Description: Move class substitution in and out of an operation. (Contributed by NM, 12-Nov-2005.)
Assertion
Ref Expression
csbov2g  |-  ( A  e.  V  ->  [_ A  /  x ]_ ( B F C )  =  ( B F [_ A  /  x ]_ C
) )
Distinct variable groups:    x, B    x, F
Allowed substitution hints:    A( x)    C( x)    V( x)

Proof of Theorem csbov2g
StepHypRef Expression
1 csbov12g 5814 . 2  |-  ( A  e.  V  ->  [_ A  /  x ]_ ( B F C )  =  ( [_ A  /  x ]_ B F [_ A  /  x ]_ C
) )
2 csbconstg 3017 . . 3  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )
32oveq1d 5793 . 2  |-  ( A  e.  V  ->  ( [_ A  /  x ]_ B F [_ A  /  x ]_ C )  =  ( B F
[_ A  /  x ]_ C ) )
41, 3eqtrd 2173 1  |-  ( A  e.  V  ->  [_ A  /  x ]_ ( B F C )  =  ( B F [_ A  /  x ]_ C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1332    e. wcel 1481   [_csb 3004  (class class class)co 5778
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-rex 2423  df-v 2689  df-sbc 2911  df-csb 3005  df-un 3076  df-sn 3534  df-pr 3535  df-op 3537  df-uni 3741  df-br 3934  df-iota 5092  df-fv 5135  df-ov 5781
This theorem is referenced by:  csbnegg  7980  fsummulc2  11245
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