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Theorem alex 1581
Description: Theorem 19.6 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
alex  |-  ( A. x ph  <->  -.  E. x  -.  ph )

Proof of Theorem alex
StepHypRef Expression
1 notnot 283 . . 3  |-  ( ph  <->  -. 
-.  ph )
21albii 1575 . 2  |-  ( A. x ph  <->  A. x  -.  -.  ph )
3 alnex 1552 . 2  |-  ( A. x  -.  -.  ph  <->  -.  E. x  -.  ph )
42, 3bitri 241 1  |-  ( A. x ph  <->  -.  E. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177   A.wal 1549   E.wex 1550
This theorem is referenced by:  2nalexn  1582  exnal  1583  19.3v  1677  sp  1763  hba1  1804  exists2  2370  pm10.253  27472  vk15.4j  28467  vk15.4jVD  28880
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566
This theorem depends on definitions:  df-bi 178  df-ex 1551
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