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Theorem drsb2 2085
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 2083 . 2  |-  ( x  =  y  ->  ( [ x  /  z ] ph  <->  [ y  /  z ] ph ) )
21sps 1809 1  |-  ( A. x  x  =  y  ->  ( [ x  / 
z ] ph  <->  [ y  /  z ] ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1372   [wsb 1706
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-12 1798  ax-13 1961
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-nf 1595  df-sb 1707
This theorem is referenced by:  sbcom3  2121  sb9iOLD  2144  sbal2  2188
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