Theorem rmov 2746

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 2452	. 2 |- ( E* x e. _V ph <-> E* x ( x e. _V /\ ph ) )
2		vex 2729	. . . 4 |- x e. _V
3	2	biantrur 301	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	mobii 2051	. 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*wmo 2015   e. wcel 2136   E*wrmo 2447   _Vcvv 2726

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 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-eu 2017  df-mo 2018  df-clab 2152  df-cleq 2158  df-clel 2161  df-rmo 2452  df-v 2728

This theorem is referenced by: (None)