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Theorem csbconstg 2987
Description: Substitution doesn't affect a constant  B (in which  x is not free). csbconstgf 2986 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 2258 . 2  |-  F/_ x B
21csbconstgf 2986 1  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316    e. wcel 1465   [_csb 2975
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-sbc 2883  df-csb 2976
This theorem is referenced by:  sbcel1g  2992  sbceq1g  2993  sbcel2g  2994  sbceq2g  2995  csbidmg  3026  sbcbr12g  3953  sbcbr1g  3954  sbcbr2g  3955  sbcrel  4595  csbcnvg  4693  csbresg  4792  sbcfung  5117  csbfv12g  5425  csbfv2g  5426  elfvmptrab  5484  csbov12g  5778  csbov1g  5779  csbov2g  5780
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