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Theorem exnalim 1582
Description: One direction of Theorem 19.14 of [Margaris] p. 90. In classical logic the converse also holds. (Contributed by Jim Kingdon, 15-Jul-2018.)
Assertion
Ref Expression
exnalim  |-  ( E. x  -.  ph  ->  -. 
A. x ph )

Proof of Theorem exnalim
StepHypRef Expression
1 alexim 1581 . 2  |-  ( A. x ph  ->  -.  E. x  -.  ph )
21con2i 592 1  |-  ( E. x  -.  ph  ->  -. 
A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1287   E.wex 1426
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 579  ax-in2 580  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395
This theorem is referenced by:  exanaliim  1583  alexnim  1584  dtru  4366  brprcneu  5282
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