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Theorem reuv 2816
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 2563 . 2  |-  ( E! x  e.  _V  ph  <->  E! x ( x  e. 
_V  /\  ph ) )
2 vex 2804 . . . 4  |-  x  e. 
_V
32biantrur 492 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43eubii 2165 . 2  |-  ( E! x ph  <->  E! x
( x  e.  _V  /\ 
ph ) )
51, 4bitr4i 243 1  |-  ( E! x  e.  _V  ph  <->  E! x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358    e. wcel 1696   E!weu 2156   E!wreu 2558   _Vcvv 2801
This theorem is referenced by:  riotav  6325  euen1  6947  hlimeui  21836
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-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-reu 2563  df-v 2803
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