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Theorem drex2 1911
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
dral1.1  |-  ( 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 1895 . 2  |-  ( A. x  x  =  y  ->  A. z A. x  x  =  y )
2 dral1.1 . 2  |-  ( A. x  x  =  y  ->  ( ph  <->  ps )
)
31, 2exbidh 1579 1  |-  ( A. x  x  =  y  ->  ( E. z ph  <->  E. z ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178   A.wal 1528   E.wex 1529
This theorem is referenced by:  exdistrf  1914  dfid3  4310  dropab1  27050  dropab2  27051  e2ebind  27601
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1530  df-nf 1533
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