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Theorem alexnim 1641
Description: A relationship between two quantifiers and negation. (Contributed by Jim Kingdon, 27-Aug-2018.)
Assertion
Ref Expression
alexnim  |-  ( A. x E. y  -.  ph  ->  -.  E. x A. y ph )

Proof of Theorem alexnim
StepHypRef Expression
1 exnalim 1639 . . 3  |-  ( E. y  -.  ph  ->  -. 
A. y ph )
21alimi 1448 . 2  |-  ( A. x E. y  -.  ph  ->  A. x  -.  A. y ph )
3 alnex 1492 . 2  |-  ( A. x  -.  A. y ph  <->  -. 
E. x A. y ph )
42, 3sylib 121 1  |-  ( A. x E. y  -.  ph  ->  -.  E. x A. y ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1346   E.wex 1485
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354  df-nf 1454
This theorem is referenced by:  nalset  4117  bj-nalset  13895
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