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Theorem 19.9t 1969
Description: A closed version of 19.9 1970. (Contributed by NM, 13-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) (Proof shortened by Wolf Lammen, 14-Jul-2020.)
Assertion
Ref Expression
19.9t  |-  ( F/ x ph  ->  ( E. x ph  <->  ph ) )

Proof of Theorem 19.9t
StepHypRef Expression
1 id 22 . . 3  |-  ( F/ x ph  ->  F/ x ph )
2119.9d 1968 . 2  |-  ( F/ x ph  ->  ( E. x ph  ->  ph )
)
3 19.8a 1935 . 2  |-  ( ph  ->  E. x ph )
42, 3impbid1 207 1  |-  ( F/ x ph  ->  ( E. x ph  <->  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188   E.wex 1663   F/wnf 1667
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668
This theorem is referenced by:  19.9  1970  19.9hOLD  1973  19.9dOLD  1974  19.21t  1986  19.23tOLD  1992  spimt  2097  sbft  2208  vtoclegft  3121  bj-cbv3tb  31312  bj-spimtv  31319  bj-sbftv  31376  bj-equsal1t  31424  bj-19.21t  31432
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