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Theorem 19.9v 1663
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 1529 . 2  |-  ( E. x ph  <->  -.  A. x  -.  ph )
2 19.3v 1662 . . 3  |-  ( A. x  -.  ph  <->  -.  ph )
32con2bii 322 . 2  |-  ( ph  <->  -. 
A. x  -.  ph )
41, 3bitr4i 243 1  |-  ( E. x ph  <->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wal 1527   E.wex 1528
This theorem is referenced by:  exlimdv  1664  exlimiv  1666  zfcndpow  8238  prter2  26749  rfcnnnub  27707  relopabVD  28677  bnj937  28803  bnj594  28944  bnj907  28997  bnj1128  29020  bnj1145  29023
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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