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Theorem rmov 2817
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 2564 . 2  |-  ( E* x  e.  _V ph  <->  E* x ( x  e. 
_V  /\  ph ) )
2 vex 2804 . . . 4  |-  x  e. 
_V
32biantrur 492 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43mobii 2192 . 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. wcel 1696   E*wmo 2157   E*wrmo 2559   _Vcvv 2801
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-rmo 2564  df-v 2803
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