Theorem rexv 1358

Description: An existential quantifier restricted to the universe is unrestricted.

Assertion

Ref	Expression
rexv	|- (E.x e. V ph <-> E.xph)

Proof of Theorem rexv

Step	Hyp	Ref	Expression
1		df-rex 1206	. 2 |- (E.x e. V ph <-> E.x(x e. V /\ ph))
2		visset 1350	. . . 4 |- x e. V
3	2	biantrur 544	. . 3 |- (ph <-> (x e. V /\ ph))
4	3	biex 733	. 2 |- (E.xph <-> E.x(x e. V /\ ph))
5	1, 4	bitr4 154	1 |- (E.x e. V ph <-> E.xph)

Syntax hints:   <-> wb 127   /\ wa 196  E.wex 678   e. wcel 1092  E.wrex 1202  Vcvv 1348

This theorem is referenced by:  rexcom4 1361  ac6s2 3578

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-9 799  ax-12 802  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-rex 1206  df-v 1349

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