ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbcg Unicode version

Theorem sbcg 2892
Description: Substitution for a variable not occurring in a wff does not affect it. Distinct variable form of sbcgf 2890. (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 1462 . 2  |-  F/ x ph
21sbcgf 2890 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103    e. wcel 1434   [.wsbc 2824
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-sbc 2825
This theorem is referenced by:  sbcabel  2904  csbunig  3629  csbxpg  4467  sbcfung  4975  f1od2  5907
  Copyright terms: Public domain W3C validator