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Theorem reuv 2971
Description: A uniqueness quantifier restricted to the universe is unrestricted. (Contributed by NM, 1-Nov-2010.)
Assertion
Ref Expression
reuv  |-  ( E! x  e.  _V  ph  <->  E! x ph )

Proof of Theorem reuv
StepHypRef Expression
1 df-reu 2712 . 2  |-  ( E! x  e.  _V  ph  <->  E! x ( x  e. 
_V  /\  ph ) )
2 vex 2959 . . . 4  |-  x  e. 
_V
32biantrur 493 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43eubii 2290 . 2  |-  ( E! x ph  <->  E! x
( x  e.  _V  /\ 
ph ) )
51, 4bitr4i 244 1  |-  ( E! x  e.  _V  ph  <->  E! x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    e. wcel 1725   E!weu 2281   E!wreu 2707   _Vcvv 2956
This theorem is referenced by:  riotav  6554  euen1  7177  hlimeui  22743
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-reu 2712  df-v 2958
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