Theorem rmov 2823

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 2518	. 2 |- ( E* x e. _V ph <-> E* x ( x e. _V /\ ph ) )
2		vex 2805	. . . 4 |- x e. _V
3	2	biantrur 303	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	mobii 2116	. 2 |- ( E* x ph <-> E* x ( x e. _V /\ ph ) )
5	1, 4	bitr4i 187	1 |- ( E* x e. _V ph <-> E* x ph )

Syntax hints:   /\ wa 104   <-> wb 105   E*wmo 2080   e. wcel 2202   E*wrmo 2513   _Vcvv 2802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-eu 2082  df-mo 2083  df-clab 2218  df-cleq 2224  df-clel 2227  df-rmo 2518  df-v 2804

This theorem is referenced by: (None)