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Theorem alex 1694
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 292 . . 3  |-  ( ph  <->  -. 
-.  ph )
21albii 1687 . 2  |-  ( A. x ph  <->  A. x  -.  -.  ph )
3 alnex 1661 . 2  |-  ( A. x  -.  -.  ph  <->  -.  E. x  -.  ph )
42, 3bitri 252 1  |-  ( A. x ph  <->  -.  E. x  -.  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187   A.wal 1435   E.wex 1659
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  exnal  1695  2nalexn  1696  alimex  1699  19.3v  1802  sp  1909  hba1  1950  exists2  2358  pm10.253  36396  vk15.4j  36570  vk15.4jVD  36999
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