MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  rmov Unicode version

Theorem rmov 2804
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 2551 . 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 ) )
43mobii 2179 . 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 1684   E*wmo 2144   E*wrmo 2546   _Vcvv 2788
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-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-rmo 2551  df-v 2790
  Copyright terms: Public domain W3C validator