MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbf2 Unicode version

Theorem sbf2 1968
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 1756 . 2  |-  F/ x A. x ph
21sbf 1966 1  |-  ( [ y  /  x ] A. x ph  <->  A. x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176   A.wal 1527   [wsb 1629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532  df-sb 1630
  Copyright terms: Public domain W3C validator