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Theorem reuv 2627
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 2360 . 2  |-  ( E! x  e.  _V  ph  <->  E! x ( x  e. 
_V  /\  ph ) )
2 vex 2613 . . . 4  |-  x  e. 
_V
32biantrur 297 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43eubii 1952 . 2  |-  ( E! x ph  <->  E! x
( x  e.  _V  /\ 
ph ) )
51, 4bitr4i 185 1  |-  ( E! x  e.  _V  ph  <->  E! x ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103    e. wcel 1434   E!weu 1943   E!wreu 2355   _Vcvv 2610
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-clab 2070  df-cleq 2076  df-clel 2079  df-reu 2360  df-v 2612
This theorem is referenced by:  euen1  6371  updjud  6576
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