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Theorem alexn 1590
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 1584 . . 3  |-  ( E. y  -.  ph  <->  -.  A. y ph )
21albii 1576 . 2  |-  ( A. x E. y  -.  ph  <->  A. x  -.  A. y ph )
3 alnex 1553 . 2  |-  ( A. x  -.  A. y ph  <->  -. 
E. x A. y ph )
42, 3bitri 242 1  |-  ( A. x E. y  -.  ph  <->  -. 
E. x A. y ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178   A.wal 1550   E.wex 1551
This theorem is referenced by:  2exnexn  1591  nalset  4342  kmlem2  8033
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567
This theorem depends on definitions:  df-bi 179  df-ex 1552
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