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Theorem drex2 1711
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.)
Hypothesis
Ref Expression
drex2.1  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
Assertion
Ref Expression
drex2  |-  ( A. x  x  =  y  ->  ( E. z ph  <->  E. z ps ) )

Proof of Theorem drex2
StepHypRef Expression
1 hbae 1697 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
2 drex2.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2exbidh 1594 1  |-  ( A. x  x  =  y  ->  ( E. z ph  <->  E. z ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1330   E.wex 1469
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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  exdistrfor  1773
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