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Theorem drsb2 1797
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 1796 . 2  |-  ( x  =  y  ->  ( [ x  /  z ] ph  <->  [ y  /  z ] ph ) )
21sps 1502 1  |-  ( A. x  x  =  y  ->  ( [ x  / 
z ] ph  <->  [ y  /  z ] ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1314   [wsb 1720
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721
This theorem is referenced by: (None)
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