Theorem ralv 2650

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 2375	. 2 |- ( A. x e. _V ph <-> A. x ( x e. _V -> ph ) )
2		vex 2636	. . . 4 |- x e. _V
3	2	a1bi 242	. . 3 |- ( ph <-> ( x e. _V -> ph ) )
4	3	albii 1411	. 2 |- ( A. x ph <-> A. x ( x e. _V -> ph ) )
5	1, 4	bitr4i 186	1 |- ( A. x e. _V ph <-> A. x ph )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1294   e. wcel 1445   A.wral 2370   _Vcvv 2633

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-ext 2077

This theorem depends on definitions:  df-bi 116  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-ral 2375  df-v 2635

This theorem is referenced by:  ralcom4  2655  viin  3811  issref  4847  frecrdg  6211