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Theorem alneu 27846
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 4352 . . 3  |-  ( E! x ph  ->  E. x  -.  ph )
2 exnal 1580 . . 3  |-  ( E. x  -.  ph  <->  -.  A. x ph )
31, 2sylib 189 . 2  |-  ( E! x ph  ->  -.  A. x ph )
43con2i 114 1  |-  ( A. x ph  ->  -.  E! x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1546   E.wex 1547   E!weu 2254
This theorem is referenced by:  eu2ndop1stv  27847
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-nul 4298  ax-pow 4337
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258
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