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Theorem drsb2 1764
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 1763 . 2  |-  ( x  =  y  ->  ( [ x  /  z ] ph  <->  [ y  /  z ] ph ) )
21sps 1471 1  |-  ( A. x  x  =  y  ->  ( [ x  / 
z ] ph  <->  [ y  /  z ] ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1283   [wsb 1687
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688
This theorem is referenced by: (None)
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