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Theorem alex 1697
Description: Theorem 19.6 of [Margaris] p. 89. (Contributed by NM, 12-Mar-1993.)
Assertion
Ref Expression
alex  |-  ( A. x ph  <->  -.  E. x  -.  ph )

Proof of Theorem alex
StepHypRef Expression
1 notnot 293 . . 3  |-  ( ph  <->  -. 
-.  ph )
21albii 1690 . 2  |-  ( A. x ph  <->  A. x  -.  -.  ph )
3 alnex 1664 . 2  |-  ( A. x  -.  -.  ph  <->  -.  E. x  -.  ph )
42, 3bitri 253 1  |-  ( A. x ph  <->  -.  E. x  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 188   A.wal 1441   E.wex 1662
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681
This theorem depends on definitions:  df-bi 189  df-ex 1663
This theorem is referenced by:  exnal  1698  2nalexn  1699  alimex  1702  19.3v  1812  sp  1936  hba1  1977  exists2  2390  pm10.253  36705  vk15.4j  36879  vk15.4jVD  37305
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