Theorem reuv 2307

Description: A uniqueness quantifier restricted to the universe is unrestricted.

Assertion

Ref	Expression
reuv	|- (E!x e. _V ph <-> E!xph)

Proof of Theorem reuv

Step	Hyp	Ref	Expression
1		df-reu 2111	. 2 |- (E!x e. _V ph <-> E!x(x e. _V /\ ph))
2		visset 2295	. . . 4 |- x e. _V
3	2	biantrur 794	. . 3 |- (ph <-> (x e. _V /\ ph))
4	3	eubii 1780	. 2 |- (E!xph <-> E!x(x e. _V /\ ph))
5	1, 4	bitr4i 193	1 |- (E!x e. _V ph <-> E!xph)

Syntax hints:   <-> wb 163   /\ wa 240   e. wcel 1300  E!weu 1771  E!wreu 2107  _Vcvv 2292

This theorem is referenced by:  euobj1 3834  euobj2 3835  riotav 5565  euuni2 15663

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-eu 1775  df-clab 1872  df-cleq 1877  df-clel 1880  df-reu 2111  df-v 2294

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