MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  drsb2 Unicode version

Theorem drsb2 2001
Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.)
Assertion
Ref Expression
drsb2  |-  ( A. x  x  =  y  ->  ( [ x  / 
z ] ph  <->  [ y  /  z ] ph ) )

Proof of Theorem drsb2
StepHypRef Expression
1 sbequ 2000 . 2  |-  ( x  =  y  ->  ( [ x  /  z ] ph  <->  [ y  /  z ] ph ) )
21sps 1739 1  |-  ( A. x  x  =  y  ->  ( [ x  / 
z ] ph  <->  [ y  /  z ] ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1527   [wsb 1629
This theorem is referenced by:  sb9i  2034
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-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630
  Copyright terms: Public domain W3C validator