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Theorem 19.9v 1664
Description: Special case of Theorem 19.9 of [Margaris] p. 89. (Contributed by NM, 28-May-1995.) (Revised by NM, 1-Aug-2017.)
Assertion
Ref Expression
19.9v  |-  ( E. x ph  <->  ph )
Distinct variable group:    ph, x

Proof of Theorem 19.9v
StepHypRef Expression
1 df-ex 1530 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
2 19.3v 1663 . . 3  |-  ( A. x  -.  ph  <->  -.  ph )
32con2bii 324 . 2  |-  ( ph  <->  -. 
A. x  -.  ph )
41, 3bitr4i 245 1  |-  ( E. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178   A.wal 1528   E.wex 1529
This theorem is referenced by:  exlimdv  1665  exlimiv  1667  zfcndpow  8233  prter2  26148  rfcnnnub  27106  relopabVD  27945  bnj937  28070  bnj594  28211  bnj907  28264  bnj1128  28287  bnj1145  28290
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
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1530
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