Theorem rexv 1812

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 1642	. 2 |- (E.x e. V ph <-> E.x(x e. V /\ ph))
2		visset 1804	. . . 4 |- x e. V
3	2	biantrur 723	. . 3 |- (ph <-> (x e. V /\ ph))
4	3	exbii 1047	. 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 955  E.wex 977  E.wrex 1638  Vcvv 1802

This theorem is referenced by:  rexcom4 1815  ac6s2 4730

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-rex 1642  df-v 1803

Copyright terms: Public domain