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Theorem sbcg 2973
 Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf 2971. (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 1508 . 2 𝑥𝜑
21sbcgf 2971 1 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝜑))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104   ∈ wcel 1480  [wsbc 2904 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-sbc 2905 This theorem is referenced by:  sbcabel  2985  csbunig  3739  csbxpg  4615  sbcfung  5142  f1od2  6125
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