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Theorem rmov 2591
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 2331 . 2  |-  ( E* x  e.  _V  ph  <->  E* x ( x  e. 
_V  /\  ph ) )
2 vex 2577 . . . 4  |-  x  e. 
_V
32biantrur 291 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43mobii 1953 . 2  |-  ( E* x ph  <->  E* x
( x  e.  _V  /\ 
ph ) )
51, 4bitr4i 180 1  |-  ( E* x  e.  _V  ph  <->  E* x ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 101    <-> wb 102    e. wcel 1409   E*wmo 1917   E*wrmo 2326   _Vcvv 2574
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-eu 1919  df-mo 1920  df-clab 2043  df-cleq 2049  df-clel 2052  df-rmo 2331  df-v 2576
This theorem is referenced by: (None)
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