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Theorem rmov 2916
Description: A uniqueness quantifier restricted to the universe is unrestricted. (Contributed by Alexander van der Vekens, 17-Jun-2017.)
Assertion
Ref Expression
rmov  |-  ( E* x  e.  _V ph  <->  E* x ph )

Proof of Theorem rmov
StepHypRef Expression
1 df-rmo 2658 . 2  |-  ( E* x  e.  _V ph  <->  E* x ( x  e. 
_V  /\  ph ) )
2 vex 2903 . . . 4  |-  x  e. 
_V
32biantrur 493 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43mobii 2275 . 2  |-  ( E* x ph  <->  E* x
( x  e.  _V  /\ 
ph ) )
51, 4bitr4i 244 1  |-  ( E* x  e.  _V ph  <->  E* x ph )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    /\ wa 359    e. wcel 1717   E*wmo 2240   E*wrmo 2653   _Vcvv 2900
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-11 1753  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2243  df-mo 2244  df-clab 2375  df-cleq 2381  df-clel 2384  df-rmo 2658  df-v 2902
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