Theorem ralv 1820

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

Assertion

Ref	Expression
ralv	|- (A.x e. V ph <-> A.xph)

Proof of Theorem ralv

Step	Hyp	Ref	Expression
1		df-ral 1649	. 2 |- (A.x e. V ph <-> A.x(x e. V -> ph))
2		visset 1813	. . . 4 |- x e. V
3	2	a1bi 197	. . 3 |- (ph <-> (x e. V -> ph))
4	3	albii 999	. 2 |- (A.xph <-> A.x(x e. V -> ph))
5	1, 4	bitr4 176	1 |- (A.x e. V ph <-> A.xph)

Syntax hints:   -> wi 3   <-> wb 146  A.wal 954   e. wcel 958  A.wral 1645  Vcvv 1811

This theorem is referenced by:  ralcom4 1823

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-ral 1649  df-v 1812

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