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Theorem alneu 27957
Description: If a statement holds for all sets, there is not a unique set for which the statement holds. (Contributed by Alexander van der Vekens, 28-Nov-2017.)
Assertion
Ref Expression
alneu  |-  ( A. x ph  ->  -.  E! x ph )

Proof of Theorem alneu
StepHypRef Expression
1 eunex 4394 . . 3  |-  ( E! x ph  ->  E. x  -.  ph )
2 exnal 1584 . . 3  |-  ( E. x  -.  ph  <->  -.  A. x ph )
31, 2sylib 190 . 2  |-  ( E! x ph  ->  -.  A. x ph )
43con2i 115 1  |-  ( A. x ph  ->  -.  E! x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1550   E.wex 1551   E!weu 2283
This theorem is referenced by:  eu2ndop1stv  27958
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-nul 4340  ax-pow 4379
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287
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