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Theorem alex 1570
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 284 . . 3  |-  ( ph  <->  -. 
-.  ph )
21albii 1554 . 2  |-  ( A. x ph  <->  A. x  -.  -.  ph )
3 alnex 1569 . 2  |-  ( A. x  -.  -.  ph  <->  -.  E. x  -.  ph )
42, 3bitri 242 1  |-  ( A. x ph  <->  -.  E. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178   A.wal 1532   E.wex 1537
This theorem is referenced by:  2nalexn  1571  exnal  1572  exists2  2203  pm10.253  26723  vk15.4j  26984  vk15.4jVD  27380
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536
This theorem depends on definitions:  df-bi 179  df-ex 1538
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