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Theorem exnalim 1625
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 1624 . 2  |-  ( A. x ph  ->  -.  E. x  -.  ph )
21con2i 616 1  |-  ( E. x  -.  ph  ->  -. 
A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1329   E.wex 1468
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 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437
This theorem is referenced by:  exanaliim  1626  alexnim  1627  dtru  4475  brprcneu  5414  bj-nnal  12979
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