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Theorem rexv 2802
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 2549 . 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 ) )
43exbii 1569 . 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.wex 1528    e. wcel 1684   E.wrex 2544   _Vcvv 2788
This theorem is referenced by:  rexcom4  2807  spesbc  3072  dfco2  5172  dfco2a  5173  dffv2  5592  exopxfr  6183  finacn  7677  ac6s2  8113  ptcmplem3  17748  hlimeui  21820  rexcom4f  23134  isrnsigaOLD  23473  isrnsiga  23474  prdstotbnd  26518  moxfr  26752  eldioph2b  26842  kelac1  27161  cbvexsv  28312
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-ex 1529  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-rex 2549  df-v 2790
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