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Theorem alneu 28082
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 4219 . . 3  |-  ( E! x ph  ->  E. x  -.  ph )
2 exnal 1564 . . 3  |-  ( E. x  -.  ph  <->  -.  A. x ph )
31, 2sylib 188 . 2  |-  ( E! x ph  ->  -.  A. x ph )
43con2i 112 1  |-  ( A. x ph  ->  -.  E! x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530   E.wex 1531   E!weu 2156
This theorem is referenced by:  eu2ndop1stv  28083
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-nul 4165  ax-pow 4204
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160
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