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Theorem 19.9t 1604
Description: A closed version of 19.9 1606. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortended by Wolf Lammen, 30-Dec-2017.)
Assertion
Ref Expression
19.9t  |-  ( F/ x ph  ->  ( E. x ph  <->  ph ) )

Proof of Theorem 19.9t
StepHypRef Expression
1 df-nf 1420 . . 3  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 19.9ht 1603 . . 3  |-  ( A. x ( ph  ->  A. x ph )  -> 
( E. x ph  ->  ph ) )
31, 2sylbi 120 . 2  |-  ( F/ x ph  ->  ( E. x ph  ->  ph )
)
4 19.8a 1552 . 2  |-  ( ph  ->  E. x ph )
53, 4impbid1 141 1  |-  ( F/ x ph  ->  ( E. x ph  <->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   F/wnf 1419   E.wex 1451
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-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470
This theorem depends on definitions:  df-bi 116  df-nf 1420
This theorem is referenced by:  19.9d  1622  19.23t  1638  spimt  1697  exdistrfor  1754  sbequi  1793  sbft  1802  vtoclegft  2730  copsexg  4134
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