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Theorem alexnim 1582
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 1580 . . 3  |-  ( E. y  -.  ph  ->  -. 
A. y ph )
21alimi 1387 . 2  |-  ( A. x E. y  -.  ph  ->  A. x  -.  A. y ph )
3 alnex 1431 . 2  |-  ( A. x  -.  A. y ph  <->  -. 
E. x A. y ph )
42, 3sylib 120 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 1285   E.wex 1424
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293  df-nf 1393
This theorem is referenced by:  nalset  3944  bj-nalset  11224
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