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Theorem sbcg 3142
Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf 3140. (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 1624 . 2  |-  F/ x ph
21sbcgf 3140 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    e. wcel 1715   [.wsbc 3077
This theorem is referenced by:  sbcabel  3154  csbunig  3937  csbxpg  4819  csbxpgVD  28422  csbunigVD  28426  bnj89  28499  bnj525  28519  cdlemk40  31165  cdlemkid3N  31181  cdlemkid4  31182
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-ext 2347
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-clab 2353  df-cleq 2359  df-clel 2362  df-nfc 2491  df-v 2875  df-sbc 3078
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