Theorem rexv 1821

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 1650	. 2 |- (E.x e. V ph <-> E.x(x e. V /\ ph))
2		visset 1813	. . . 4 |- x e. V
3	2	biantrur 725	. . 3 |- (ph <-> (x e. V /\ ph))
4	3	exbii 1051	. 2 |- (E.xph <-> E.x(x e. V /\ ph))
5	1, 4	bitr4 176	1 |- (E.x e. V ph <-> E.xph)

Syntax hints:   <-> wb 146   /\ wa 223   e. wcel 958  E.wex 980  E.wrex 1646  Vcvv 1811

This theorem is referenced by:  rexcom4 1824  ac6s2 4758

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-rex 1650  df-v 1812

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