Theorem ralv 3219

Description: A universal quantifier restricted to the universe is unrestricted. (Contributed by NM, 26-Mar-2004.)

Assertion

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

Proof of Theorem ralv

Step	Hyp	Ref	Expression
1		df-ral 2917	. 2 |- ( A. x e. _V ph <-> A. x ( x e. _V -> ph ) )
2		vex 3203	. . . 4 |- x e. _V
3	2	a1bi 352	. . 3 |- ( ph <-> ( x e. _V -> ph ) )
4	3	albii 1747	. 2 |- ( A. x ph <-> A. x ( x e. _V -> ph ) )
5	1, 4	bitr4i 267	1 |- ( A. x e. _V ph <-> A. x ph )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   e. wcel 1990   A.wral 2912   _Vcvv 3200

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-ral 2917  df-v 3202

This theorem is referenced by:  ralcom4  3224  viin  4579  issref  5509  ralcom4f  29316  hfext  32290  clsk1independent  38344  ntrneiel2  38384  ntrneik4w  38398