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Theorem sbcg 3228
Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf 3226. (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 1630 . 2  |-  F/ x ph
21sbcgf 3226 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178    e. wcel 1726   [.wsbc 3163
This theorem is referenced by:  sbcabel  3240  csbunig  4025  csbxpg  4908  sbcfun  27977  csbxpgVD  29080  csbunigVD  29084  bnj89  29160  bnj525  29180  bnj1128  29433  cdlemk40  31788  cdlemkid3N  31804  cdlemkid4  31805
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164
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