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Theorem csbconstg 2945
Description: Substitution doesn't affect a constant  B (in which  x is not free). csbconstgf 2944 with distinct variable requirement. (Contributed by Alan Sare, 22-Jul-2012.)
Assertion
Ref Expression
csbconstg  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )
Distinct variable group:    x, B
Allowed substitution hints:    A( x)    V( x)

Proof of Theorem csbconstg
StepHypRef Expression
1 nfcv 2228 . 2  |-  F/_ x B
21csbconstgf 2944 1  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1289    e. wcel 1438   [_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-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:  sbcel1g  2950  sbceq1g  2951  sbcel2g  2952  sbceq2g  2953  csbidmg  2984  sbcbr12g  3895  sbcbr1g  3896  sbcbr2g  3897  sbcrel  4524  csbcnvg  4620  csbresg  4716  sbcfung  5039  csbfv12g  5340  csbfv2g  5341  csbov12g  5688  csbov1g  5689  csbov2g  5690
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