ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbf2 Unicode version

Theorem sbf2 1788
Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005.)
Assertion
Ref Expression
sbf2  |-  ( [ y  /  x ] A. x ph  <->  A. x ph )

Proof of Theorem sbf2
StepHypRef Expression
1 nfa1 1551 . 2  |-  F/ x A. x ph
21sbf 1787 1  |-  ( [ y  /  x ] A. x ph  <->  A. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 105   A.wal 1361   [wsb 1772
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-i9 1540  ax-ial 1544
This theorem depends on definitions:  df-bi 117  df-nf 1471  df-sb 1773
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator