Theorem rmov 2791

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 2491	. 2 |- ( E* x e. _V ph <-> E* x ( x e. _V /\ ph ) )
2		vex 2774	. . . 4 |- x e. _V
3	2	biantrur 303	. . 3 |- ( ph <-> ( x e. _V /\ ph ) )
4	3	mobii 2090	. 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 2054   e. wcel 2175   E*wrmo 2486   _Vcvv 2771

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-eu 2056  df-mo 2057  df-clab 2191  df-cleq 2197  df-clel 2200  df-rmo 2491  df-v 2773

This theorem is referenced by: (None)