Theorem rmov 2701

Description: An at-most-one 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

Step	Hyp	Ref	Expression
1		df-rmo 2422	. 2 |- ( E* x e. _V ph <-> E* x ( x e. _V /\ ph ) )
2		vex 2684	. . . 4 |- x e. _V
3	2	biantrur 301	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	mobii 2034	. 2 |- ( E* x ph <-> E* x ( x e. _V /\ ph ) )
5	1, 4	bitr4i 186	1 |- ( E* x e. _V ph <-> E* x ph )

Syntax hints:   /\ wa 103   <-> wb 104   e. wcel 1480   E*wmo 1998   E*wrmo 2417   _Vcvv 2681

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001  df-clab 2124  df-cleq 2130  df-clel 2133  df-rmo 2422  df-v 2683

This theorem is referenced by: (None)