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Theorem reuv 2803
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 2550 . 2  |-  ( E! x  e.  _V  ph  <->  E! x ( x  e. 
_V  /\  ph ) )
2 vex 2791 . . . 4  |-  x  e. 
_V
32biantrur 492 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43eubii 2152 . 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 1684   E!weu 2143   E!wreu 2545   _Vcvv 2788
This theorem is referenced by:  riotav  6309  euen1  6931  hlimeui  21820
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-reu 2550  df-v 2790
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