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Theorem alneu 38757
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 4613 . . 3  |-  ( E! x ph  ->  E. x  -.  ph )
2 exnal 1710 . . 3  |-  ( E. x  -.  ph  <->  -.  A. x ph )
31, 2sylib 201 . 2  |-  ( E! x ph  ->  -.  A. x ph )
43con2i 125 1  |-  ( A. x ph  ->  -.  E! x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1453   E.wex 1674   E!weu 2310
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-8 1900  ax-9 1907  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-nul 4550  ax-pow 4598
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1458  df-ex 1675  df-nf 1679  df-eu 2314  df-mo 2315
This theorem is referenced by:  eu2ndop1stv  38758
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