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Theorem rexv 2618
Description: An existential quantifier restricted to the universe is unrestricted. (Contributed by NM, 26-Mar-2004.)
Assertion
Ref Expression
rexv  |-  ( E. x  e.  _V  ph  <->  E. x ph )

Proof of Theorem rexv
StepHypRef Expression
1 df-rex 2355 . 2  |-  ( E. x  e.  _V  ph  <->  E. x ( x  e. 
_V  /\  ph ) )
2 vex 2605 . . . 4  |-  x  e. 
_V
32biantrur 297 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43exbii 1537 . 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.wex 1422    e. wcel 1434   E.wrex 2350   _Vcvv 2602
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 2064
This theorem depends on definitions:  df-bi 115  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-rex 2355  df-v 2604
This theorem is referenced by:  rexcom4  2623  spesbc  2900  dfco2  4850  dfco2a  4851
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