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Theorem sbcg 2908
Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf 2906. (Contributed by Alan Sare, 10-Nov-2012.)
Assertion
Ref Expression
sbcg  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ph ) )
Distinct variable group:    ph, x
Allowed substitution hints:    A( x)    V( x)

Proof of Theorem sbcg
StepHypRef Expression
1 nfv 1466 . 2  |-  F/ x ph
21sbcgf 2906 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    e. wcel 1438   [.wsbc 2840
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
This theorem is referenced by:  sbcabel  2920  csbunig  3661  csbxpg  4519  sbcfung  5039  f1od2  6000
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