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Theorem alexn 1566
Description: A relationship between two quantifiers and negation. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
alexn  |-  ( A. x E. y  -.  ph  <->  -. 
E. x A. y ph )

Proof of Theorem alexn
StepHypRef Expression
1 exnal 1561 . . 3  |-  ( E. y  -.  ph  <->  -.  A. y ph )
21albii 1553 . 2  |-  ( A. x E. y  -.  ph  <->  A. x  -.  A. y ph )
3 alnex 1530 . 2  |-  ( A. x  -.  A. y ph  <->  -. 
E. x A. y ph )
42, 3bitri 240 1  |-  ( A. x E. y  -.  ph  <->  -. 
E. x A. y ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176   A.wal 1527   E.wex 1528
This theorem is referenced by:  2exnexn  1567  nalset  4151  kmlem2  7777
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-ex 1529
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