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Theorem sbcg 3111
 Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf 3109. (Contributed by Alan Sare, 10-Nov-2012.)
Assertion
Ref Expression
sbcg (A V → ([̣A / xφφ))
Distinct variable group:   φ,x
Allowed substitution hints:   A(x)   V(x)

Proof of Theorem sbcg
StepHypRef Expression
1 nfv 1619 . 2 xφ
21sbcgf 3109 1 (A V → ([̣A / xφφ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∈ wcel 1710  [̣wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by:  sbcabel  3123  csbunig  3899  csbxpg  4813
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