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

Theorem rmov 2964
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 2705 . 2  |-  ( E* x  e.  _V ph  <->  E* x ( x  e. 
_V  /\  ph ) )
2 vex 2951 . . . 4  |-  x  e. 
_V
32biantrur 493 . . 3  |-  ( ph  <->  ( x  e.  _V  /\  ph ) )
43mobii 2316 . 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 1725   E*wmo 2281   E*wrmo 2700   _Vcvv 2948
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-rmo 2705  df-v 2950
  Copyright terms: Public domain W3C validator