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Theorem exnal 1621
Description: Theorem 19.14 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
exnal  |-  ( E. x  -.  ph  <->  -.  A. x ph )

Proof of Theorem exnal
StepHypRef Expression
1 alex 1620 . 2  |-  ( A. x ph  <->  -.  E. x  -.  ph )
21con2bii 332 1  |-  ( E. x  -.  ph  <->  -.  A. x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184   A.wal 1360   E.wex 1589
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1594  ax-4 1605
This theorem depends on definitions:  df-bi 185  df-ex 1590
This theorem is referenced by:  alexn  1631  exanali  1637  19.30  1658  excom  1786  nfeqf2  1988  nabbi  2696  spc3gv  3051  notzfaus  4455  dtru  4471  eunex  4473  reusv2lem2  4482  dtruALT  4512  dvdemo1  4515  dtruALT2  4524  brprcneu  5672  dffv2  5752  zfcndpow  8771  hashfun  12183  nmo  25693  axrepprim  27200  axunprim  27201  axregprim  27203  axinfprim  27204  axacprim  27205  dftr6  27407  brtxpsd  27772  elfuns  27793  dfrdg4  27828  alneu  29871  vk15.4j  30934  vk15.4jVD  31352  bnj1304  31515  bnj1253  31710  bj-dtru  31938  bj-eunex  31940  bj-dvdemo1  31943
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