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Theorem sbcg 3489
Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf 3487. (Contributed by Alan Sare, 10-Nov-2012.)
Assertion
Ref Expression
sbcg (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝜑))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝐴(𝑥)   𝑉(𝑥)

Proof of Theorem sbcg
StepHypRef Expression
1 nfv 1840 . 2 𝑥𝜑
21sbcgf 3487 1 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wcel 1987  [wsbc 3421
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-v 3191  df-sbc 3422
This theorem is referenced by:  sbcabel  3502  csbuni  4437  csbxp  5166  sbcfung  5876  fmptsnd  6395  f1od2  29365  bnj89  30530  bnj525  30550  bnj1128  30801  csbwrecsg  32840  csbrdgg  32842  csboprabg  32843  mptsnunlem  32852  topdifinffinlem  32862  relowlpssretop  32879  rdgeqoa  32885  csbfinxpg  32892  sbtru  33575  sbfal  33576  cdlemk40  35720  cdlemkid3N  35736  cdlemkid4  35737  frege70  37744  frege77  37751  frege116  37790  frege118  37792  trsbc  38267  csbunigOLD  38569  csbxpgOLD  38571  csbxpgVD  38648  csbunigVD  38652
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