Theorem ralv 2794

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 2491	. 2 |- ( A. x e. _V ph <-> A. x ( x e. _V -> ph ) )
2		vex 2779	. . . 4 |- x e. _V
3	2	a1bi 243	. . 3 |- ( ph <-> ( x e. _V -> ph ) )
4	3	albii 1494	. 2 |- ( A. x ph <-> A. x ( x e. _V -> ph ) )
5	1, 4	bitr4i 187	1 |- ( A. x e. _V ph <-> A. x ph )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1371   e. wcel 2178   A.wral 2486   _Vcvv 2776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-ral 2491  df-v 2778

This theorem is referenced by:  ralcom4  2799  viin  4001  issref  5084  frecrdg  6517