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Theorem reuv 3129
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 2821 . 2  |-  ( E! x  e.  _V  ph  <->  E! x ( x  e. 
_V  /\  ph ) )
2 vex 3116 . . . 4  |-  x  e. 
_V
32biantrur 506 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43eubii 2300 . 2  |-  ( E! x ph  <->  E! x
( x  e.  _V  /\ 
ph ) )
51, 4bitr4i 252 1  |-  ( E! x  e.  _V  ph  <->  E! x ph )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369    e. wcel 1767   E!weu 2275   E!wreu 2816   _Vcvv 3113
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-12 1803  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-clab 2453  df-cleq 2459  df-clel 2462  df-reu 2821  df-v 3115
This theorem is referenced by:  euen1  7586  hlimeui  25931
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