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Theorem drsb2 2139
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 2138 . 2  |-  ( x  =  y  ->  ( [ x  /  z ] ph  <->  [ y  /  z ] ph ) )
21sps 1770 1  |-  ( A. x  x  =  y  ->  ( [ x  / 
z ] ph  <->  [ y  /  z ] ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1549   [wsb 1658
This theorem is referenced by:  sb9i  2169
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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